Hi Don! Solfege is, indeed, a very useful skill!
That being said, you can absolutely start training it by yourself, without formal training.
If you want to use fixed-do solfege, simply learn the names for individual notes: C = do, D = re, E = mi, F = fa, G = sol, A = la, B = si (or ti if you are in the US) and you're good to go!
Start humming melodies from your pieces using these names instead of the letter names you might be more familiar with, and there you go: you're doing solfege work!
Feel free to start by singing individual notes, making sure you are really singing the correct pitch before you move on to more complicated things. Slow practice and patience are always useful, just like when learning guitar music! You can also practice some simple scales to get yourself better acquainted with the names at the very beginning.
If you are trying to learn moveable-do solfege, that is a bit more complicated, but also not too difficult - it just takes a tiny bit of theory to make sense of the note names.
Perhaps Ashley (Ash) Lucero can help with some online resource recommendations for solfege of all kinds? Since she teaches music theory at a college level.
Hope this helps!
Old thread, but still. First up, good question. Singing is absolutely the way to go. Solfege is useful for sight-singing. Guitar, like the piano, harp, percussion, does not need to concern itself with intonation: once the instrument is in tune, it's in tune. Solfege is very helpful for developing intonation skills, which is something we guitarists don't need (unliss maybe you are bending strings) With Solfege, we learn to hear the primacy of the tonic and the relationship between the tones of scale. Learn it by all means, but it takes time. Keep singing!