Hello, I hope this is the right thread.
I've been playing the guitar (classical and electric) in a band for about 7 years.

For years, all my practice time was, and still is, dedicated to band material.

That's why, when I'm alone and I'm asked to play something, I stutter and avoid playing.
I can't play band songs, because my part is never enough alone - I need the whole band in order for it to be nice.

Now I'm starting to lose interest in playing the guitar, because I don't know how to play it without the band.

I'm here to ask your help - I'm not a classical music guitarist, so what is there to be played on guitar without a band?
I don't sing, so no chords.

I'm frustrated, and every little advice is helpful.
Thank you in advance.
Why don't you practice something new, like fingerstyle stuff that UG's been promoting?
No chords, so I guess we're talking fingerstyle, right?

You could always go to your local music store and ask them what sheet music they have for classical guitar. I got taught classical guitar for a few years before I started playing contemporary songs. Just from a quick look into my sheet music folder, there's lots and lots of classical music to be played without singing. 

Traditional Spanish guitar music is always nice to be played, or if that's not what you want, go older - look up Matteo Carcassi and Jean-Antoine Meissonnier, both of them have written lots of songs for classical guitar. If you're more into modern music, you could try and learn this thing Igor Presnyakov and Andrew Foy do - playing modern songs in a fingerstyle way that incorporates the vocal melody.