You can sand them by hand. Start with 220 dry paper or a sanding sponge that will work when wet. Progress to wet sanding with 320, 400 and 600. Just like sanding wood with the grain you should sand consistently in one direction. It won't take long, the bronze is pretty soft. It will shine like a mirror when you are done. If you don't spray it with a clear acrylic sealer it will begin to age and get that nice bronze patina that needs nothing more than a fresh water rinse or a little vinegar and water wash to keep it from getting crusty with salt. Photo of what I did with 220 dry sandpaper attached, if that level of finish works for you then go for it. If you take it to 600 grit wet sand it will look even finer.
OK now that you saved yourself some dough by sandblasting, you can spend a bunch of time repairing the damage you just caused. Penny wise $ foolish. Sorry JMHO
Toplicht has the same one.
Helmsman's folding seat at Toplicht
Some good comments and ideas here...
Source for side mounted folding helm seat?
just for fun, the old Wilcox Crittendon catalog