Anything made of suitable metal can be made sharp enough to shave. My 15" 1/2" thick Ang Khola, 18" 1/2" thick Bhojpuri and 18" 7/16" thick M-43 can all shave hair off my legs... hell, even my camp ax (which I don't use anymore) could shave
You can set up a cheap convex sharpener by tacking or taping sandpaper to a mousepad and putting that on a flat surface. The only thing you'll probably need to pay for in this setup is the sandpaper: a 3M assorted wet/dry pack ( sheets of 220, 400, 800, 1000 grits) only costs $5ish. Sharpen the blade at roughly 18ish degrees per side without adding too much pressure onto the blade - the give of the mousepad will convex the edge with a ~21ish degree final angle. Do all the work (this means creating a bur) with 220 grit - only use the higher papers to refine/polish the edge you establish. Once you finish with the 1000 grit, use an old leather belt to strop the bur off - be sure to keep the belt taught and to use minimal pressure!
For the basic technique using the above method, check out
this video. Remember he's only refining the convex edge - not establishing one. The technique is the same though, you just need to start at 220 and remember not to move on to higher grits until you can feel the bur you've created using 220! If you move on too early, you'll just find yourself with a dull (albeit shiny) edge!
You can see my setup in the background of this picture - I'm too lazy to snap another one:
Here's the end result of your efforts - My m43 can shave with ease and still hit a tree full force without any visible edge damage: