I tried this in the past and I don’t think the Bahco blades are a direct replacement for Sharks.
I have a couple of roughly similar saws, the 10 5/8” versions with the plastic top edge.
Markings are:
Bahco Prof Cut Pull Saw 10 5/8” 18 Teeth / 19 Points
Shark Pullsaw Fine cut saw 10 5/8 IN 17 PT, when the blade was pulled out the replacement number on that normally hidden part of the blade is the one you quote item no #10-2410
The blade profiles are identical at the handle end but the Bahco uses a threaded fastener in a slightly larger hole and slot. The Bahco blade will clip into the SHARK handle but it isn’t rigid and will jiggle back and forth. I’ll try to post a couple of photos of the different end slots eventually (I’m ill at present and can’t easily get out to the shed)
I'd also be interested if anyone has a source for Shark blades, I have a couple of other Shark saws and I like them.
Jim