I changed the pots in my old strat ages ago and I was pretty damn happy with the result.... you could be too.
But yes sir, A router is pretty much the only way to go. You might also want to get the routing templates for making humbucker cavities and a guided router bit from stewmac.com to do a more accurate job. You could even use the original pickguard and route that out to fit instead of getting a new one.
Welcome to the forums 😉