Hey, I'm brand new to the board and look forward to hearing from all of you at some point or another.
Though I am a good singer, when I sing and play guitar I sense that my frame is not altogether congruent with who I usually am. Keeping eye contact with someone throughout a song while attempting to keep my frame can be strange, since the themes of many songs tend to be deep rather than cocky and funny (I enjoy playing songs by matisyahu, The verve, ben harper, and the beatles).
I also enjoy making up songs off the cuff or even "freestyling." I use this to my advantage by writing funny songs about the girl I'm trying to game or a situation in general. Only while doing this, I can remain congruent with my funny and cocky frame.

As long as you don't use performing as a crutch and a necessary part of your game then you will be OK. In my opinion your guitar should be left in your bedroom, so when you want to move to seduction, you have an easy excuse to bring her into your room. At that stage cocky-funny becomes less important, and by performing some melodic music it will make the girl more comfortable and attracted to you.

Or you could make your songs funny like Bo Burnham (youtube his name)

the key is, what i've picked up at least, is to be really passionate and into what you're playing. i've had virtually every girl who's had the privilege to sit in on a jam session tell me how sexy it is to see me so into it, both friends and girl's i gamed. i completely escape reality and just get lost in the music.

and dont be a performing monkey. what i often do is "ahhh.. i really need to jam now! back in 5 mins". this way she's super curious. she'll then go look for you, find you in your bedroom, jamming with your back to the door. now you see her and say something like "hey hey hey. private session. groupies only" and put your guitar down. now you have her in your room =)
she'll probably ask you why you stopped or to play some more... say "nah, im good, i just had my fix" and jump to the next thread, start kino-ing and you might get lucky!