I've taught a lot of kids that can manage sweeps with small hands (8 years old etc) so I'm not so sure that avoiding a type of playing is the right idea. If your left hand position is correct (thumb back of neck) etc.. unless you have dwarf hands you can do it. Playing with the guitar strap like you mentioned is actually the way you should have it. It might not look as cool as your guitar hanging down to your knees but look how those people play guitar lol. Also something that might help is keeping your guitar on your left leg not your right when sitting. This will help a whole lot access. Finially after enough SLOW ACCURATE repetition you will get it. Look at Shawn Lane. His hands were not so big and look how he played and the stretches he used! There are many other examples. Having small hands is not an excuse for not playing a certain tech. Also btw all the more reason to use your pinky if you have small hands or big hands. If there are 4 frets then make sure you are using your pinky on that fourth fret! And for picking with big hands that is not an excuse as well. Just look at Itzach Pearlman how he fingers the violin with those fat fingers ahah all scrunched up on each other. Never sacrifice proper tech for nothing.

Just so you see I practice what I preach here is a latest video of some playing of mine. This is what I mean proper tech:


Shred Zone:

http://www.youtube.com/watch?v=NGuXfMijZKY

ALso another one:

(Live entire song)

http://www.youtube.com/watch?v=6Q8rU-13eC4