The sword is used to represent the masculine element air, in tarot. Air is both the mental realm of ideas and other ethereal or spirit worlds. The sword then signifies also the mind's ability to separate (cut), to discriminate, what I call "this, not that". Its essential role is creating duality in the mind, an event that occurs when we judge things and categorize them as good or bad, basically.
Since the archetypal feminine (for definition of archetype see Metaphor 101 page, here) is the connecting principle, women often need to develop their ability to discriminate as part of their development towards balance and wisdom. This is the meaning of fairy tale tasks of sorting grains, etc. Women need to learn to disconnect from the world, from relationships, from watery emotions. The old woman in the tower has definitely done that. The hermit or contemplative is socially disconnected, an ability which coincides with soul connection and/or connection with the Divine. We're not talking Scrooge here, a hermit who has managed to connect strongly to his worldly accumulation of cash and other investments. In my book Poetry in Motion (here) I review Certified Copy, a film story by Abbas Kiarostami about masculine and feminine ways of being that includes the woman's initiation into a more balanced way of being that includes the ability to disconnect from "the world".
If there were any woundings happening in Sleeping Beauty, the sword would speak of that, of sacrifice. However, we don't have any blood, any slicing of bodies; in fact, the Grimms' version has no description of the prince whatsoever. No sword, no armor, just a guy who heard an old man talking about the princess, the old man being another reference to the development of mature wisdom.
In Sleeping Beauty's awakening palace, things are actually a little complicated, because of the very general nature of the tale. The loving kiss of the prince is meant to signify a moment that could occur at any point in a woman's life, for one thing. Though Briar Rose is an adolescent, and the first bigtime initation after childhood typically occurs in adolescence, sometimes through falling in love, there are many women and men who do not experience a deep soul initiation in adolescence. They conform, instead, to the parentally (specifically patriarchal) oriented society described by this fairy tale kingdom that prizes safety and security above soul-connecting plunges into the dark, or even into aloneness and contemplation and not-doing. Or perhaps it is just not their fate.
The other complication as to interpretation of initiation stories that feature adolescents in general, is that the soul connected adult will ideally have a number of deeply soul connected experiences which will constitute initiations into new ways of being in the world, such as the experience of the parents referred to in the opening of the story. We can't go along assuming the story's just about Briar Rose: Adolescent. However, if we are lacking connection with the sacred, we'll make even deeply initiative experiences such as childbirth and parenting into another reason to go shopping. It could be another excuse to avoid suffering, inconvenience, and fear of death through scheduled medical childbirth, for example. We could assume our child is really ours, rather than a child of the universe entrusted to our care, and on and on. We could die of old age never having understood the beauty of the spiraling journey through deep transformation that the adolescent naturally embodies and signifies.
Like many such tales, Sleeping Beauty's not linear, but rather a complex weaving depicting the many initiating experiences that occur over a human lifetime, the ancient spiral referred to by the drop spindle which bobs up and down as it spins rather than turning straight like the wheel, and by the spiraling tower staircase Briar Rose climbs.
Though I think most folks in my society would imagine this prince as some sort of hero figure (can't remember if that's the case in Disney's version, but I'm going to guess it is), "rescuing" Briar Rose, this gentle picture of an adoring prince above lets us in on the truth of the tale. Briar Rose's prince could have been a nerd, an old man, basically anyone. For one of the themes of the story is that force is not wanted in the realms of soul connection. In that, Briar Rose is wise in her passivity, and in that way has something to teach the masculine fiery aspect. The point to wisdom is balance between the masculine and feminine. The Grimms write "From time to time a prince would try to force his way through the hedge to get to the castle. But no one ever succeeded...the young men who tried got caught...They died an agonizing death." These are the young valiants depicted in Burne-Jones's painting above, lying in a pathetic jumble on the ground.
What are the briars? They hold the intertwined concepts of defenses, of suffering, and of fear. We naturally develop fear and defenses out of our suffering, our wounding, as we go through life. The prince says, "I am not afraid. I am going to find that castle..." Here's another pointer; the alchemical meeting beyond dualistic experience is also the facing of fear. That's how we eliminate the need for heavy defenses that keep us from experiencing deeply soul, or love, or the inner self, the Divine within whether feminine or masculine. If we're afraid of going inside, we miss not only the fear, but also the love. The Grimms' prince faces the fear without so much as a sword, and in that unarmed state, he is gained access to love; "he found big, beautiful flowers". Flowering is a symbolic reference to some sort of beautiful spiritual/ethereal event within.
Well that's pretty much a wrap. Notice the mention of the kitchen, the cook and the fire that stops in the castle, references to the inner alchemical process. Through avoidance of our initiations which require removing ourselves from the world, we block our inner alchemy. We don't update our defenses formed from long past events and enter the moment.