If you did have a bass to do it to you you probably have to do some wood filling (depending how many screws it has), pop the bridge in the same location to keep the scale length, change the nut. As far as pick ups go, will if it had blades, flat magnets and not pole pieces then it matters less exactly where the strings are over the pick up. Being off pole pieces and not central is not a huge issue, it gives a different sound, and may not be as consistent so you may have to tinker. Some basses are deliberately lined up not directly over the pole pieces - Sting Ray Old Smoothie as an example.
so far as the neck profile, that’s completely up to you, there are flat radius ones out there, remember you can always shave an existing neck down to your requirements should you find the right bass, but not quite right neck