Is there a way to smooth without making holes in a face? First of all, I can't add or delete vertices or change vertex order because otherwise I'll mess up the UV mapping for this mesh, which I can't do anything about because it's applied by an external program (this is a skyrim model, the program is Outfit Studio). 

This is what I'm dealing with. The left-hand side of the torso is all in one piece, but for whatever reason the right-hand side is multiple disconnected pieces. The unselected parts are the "seams" where the mesh splits.



This is what it looks like if I select everything.



And then if I apply smooth.



The left-hand side is fine because it's one piece, but if I smooth the right-hand side the pieces of the mesh end up shrinking. How do I get the right side looking like the left side without changing the vertices?
to me it lokes like you have double Vertices. You should make a copy file (just in case you mess it up) and select all Vertices with 'a' and on the left side you should have a panel (you can let it show up with 't', that's how it workes in blender). Select 'Tool' and under 'Mesh Tools' you should find the option 'Remove:' and there is the button 'Remouve Doubles'.

I hope that should fix it for you.
Gr W.Zayde