Go to the mall with her, walk by the aisle where they sell shaving products, and put a razor in the basket.
Or, go to the store yourself and buy one.
That's what I did when I wanted to use tampons instead of pads, but did not want to ask my mom. I went to the store, bought myself a box of tampons, and a few months later when she saw the box of tampons she started buying them for me when I'd run out.
Simple as that. It's your body and your choice, so either buck up and say "mom, can you buy me a razor", buy one yourself or buy one when you are shopping with your mom. All I did was use the razor heads that my mom purchased for her and my sister. There were always unopened ones, I would use them, and I never actually said "hey mom I want to shave". I've never actually told her, and it's not something you need to talk to your mom about unless you feel that you need to.
If she finds out, or you ask her, and you two talk about it, it will for sure be awkward. You might even be embarrassed. But just remember - it's a part of growing up, and you will only feel awkward for a short time, whereas your legs will remain hairy for the rest of your life. So what's worse, feeling awkward and embarrassed around your mom for a few days, or having hair legs because you don't want to buy your own or talk to her about it?