If you have a really close relationship, I think you'll find plenty of opportunity to let her know your feelings on shaving and beauty. She may already know those feelings and might feel bad about going against what you want so she's only bringing it up now as a possibility. I wanted to shave for ages but when I would casually mention it my mom would dismiss it by saying I didn't need to. I didn't feel close enough to her to say 'Hey mom, this is really important to me' though. I think a lot of the angst in our relationship is because it was hard for her to let go as I got older and not just make my own decisions, but respect them as my own. So... shaving brings up a pretty wide variety of parenting issues for me.
OP, you mentioned possibly putting some razors and shaving cream in her holiday sock... Did you wind up doing that or talking to her about it more? I think the stocking stuffer idea was a good one.
If you start shaving, you can always stop. There might be a while of awkward spikiness, but eventually you'll wind up with your same old hair back. It also avoids the chemical issue in other products. I've never used those myself. I would let my kid shave as soon as they were able to safely use a razor.