Does the Fast Fire III with the speedbead mount fit a SP10 or do you need to use a saddle type mount?
Burris doesn't make a sp10 mount for the spread bead - you will have to get a mount
What type of mount? Do the type of rails matter?
AIMTECH and B-SQUARE are the only ones I know of and both are discontinued. You can try Numrich and see if the have any. They pop up on here an eBay on occasion.
You can get the receiver tapped for a weaver rail - any competent gunsmith can perform the job
I'd get receiver drilled and tapped. You can't trust a speed bead