Super-embarrassing question, but are we talking about the inside of your thighs at the top where they rub together when you're wearing a skirt? Not sure what body-glide is or how deodorant would help, but does it work for this issue? It's been super-hot this summer and wearing compression-type shorts under my dresses is killing me.
Buy an anti-chafing product with dimethicone as the primary ingredient (there are many different brands). It is silky-smooth and dries almost instantly. You only need a pea-sized amount, so a tube lasts a long time.
I bought body glide for our first Disney trip many years ago (saw it recommended here). I put it on my feet (with croc flip flops) and didn't even make it to the bus stop before I had to go back to the room to wash it off because it was super sticky and irritating. I was very glad I hadn't tested it out on my thighs.