As a female myself, I feel like you should know that you saying "I'm not gonna use Skype/Discord/any type of voice chat because I'm a girl" is YOU asking for guys to make comments like that towards you. I use both Skype and Discord, depending on who I'm playing with at the time. Do any of them care I'm female? No, they don't. To them I'm just another friend who enjoys playing League just as they do.
In game I'm whatever gender my character is but if someone asks I'll tell them I'm female. Heck, I had a game where I was playing Vel'Koz, messed up his combo, and someone made a comment towards me about it. My friend responded with "she messed up, it happens." Someone else on our team asked how he knew I was a she and my friend told the person he's my friend. Did I care he said I'm a girl? No, because I'm perfectly fine with people knowing.
And while I have my fair share of perverted comments and rude remarks, I've always NOT CARED. Depending on the comment I'll respond with, "I have a boyfriend, try again at a later date." then ignore that person if he makes a perverted comment or say "Let me go find a care to give." if they're just being rude about a female playing video games.
I'm also in a Discord channel, where there's quite a few females who play League. Do any of them care? No. Hell, two of them are married to guys who also play League. We just laugh at the stupid shit said to us.
If you're proud of being female, these types of comments shouldn't bother you. If you can't handle them, DON'T LET PEOPLE KNOW YOU'RE FEMALE! Simple as that. I don't care, none of my FEMALE friends care, heck none of my guy friends care I'm a girl. The only ones who I know that get pissed/annoyed about people making perverted/rude comments towards me or my female friends are our significant others and our guy friends.
TL;DR, Be proud of yourself or don't let people know you're a female. Simple as that.