Installing a new Shimano compact crank on an older bottom bracket?
This assumes you mean the BB is square taper (one of many examples). Most crank pullers will do square taper, but you often need to use the tool slightly differently, such as by removing a cap. You probably can't change the spindle anyway, but you should be able to buy square taper cranks to suit you, and if not a new BB isn't too expensive.

The process is essentially the same for all vaguely modern cranks.