I wouldn't bother buying live sand. I think it's a bit of snake oil that bacteria and microfauna stay alive for months inside sealed plastic bags. It would become anoxic and everything would die.
How much live rock do you have? The rock will provide ample surface area for bacterial colonisation, so you won't be losing all that much by removing the black sand.
Removing the sand will kick up a lot of detritus, and so you're best siphoning it out during water changes. You probably can't siphon/vacuum it out all in one water changes' worth of water, but you can do it progressively over several water changes. It's ok for the tank to be pretty much bare bottomed, some tanks are bare bottomed deliberately.
Once all the black substrate is out, you can then rinse your new crushed coral sand and then handball it into the tank (powerheads off) and job done.
Get some pictures of the tank up.
Also, you can create a tank thread
to document your tank in.