What's a good cheap sander to sand the ends of wooden blinds?
As 'cheap' is one of the requirements -- I'd probably go with a random orbit or even just a vibrating palm sander.  You can get some decent models for $50-60.

I would recommending one of the 1/4 sheet models, where you can use any sand paper that you cut down to size, rather than the fancy shapes that require you to specifically buy sand paper made for that model.  (the circular random orbit might be an exception ... the holes help to clear out sawdust faster and keep the paper from getting bogged down as quickly, but if you're going for cheap, 1/4 sheet's still your best bet in the long run).

I'd loosely secure the whole bundle with a ratchet strap or something similar, jog the slats so they're well aligned (stand it on end and tap it on the ground), then tighten the strap, and sand the edges down.

If the slats are really thin, and you fear them breaking, either add another strap close to the edge, or even just bundle it up with tape.  (if you don't want to deal with tape residue, use cling film or similar first, then tape it)