How to deal with/tidy up established borders without destroying heritage planting?

Exactly that.

A couple of years ago we took on this 1930s built renovation project and after MUCH back breaking work managed to unearth original borders in the front garden and re-instate the front lawn as the whole area had devolved into a waste high mess of overgrowth (Amongst a whole bunch of internal preservation work)

All is great in the sense that the borders have Ben uncovered and have some FANTASTIC heritage planting in them, starting with waves of snowdrops, followed by daffodils, then bluebells…. The issue is, it gets to this time of year and the whole lot is mixed with weeds. The finished daffodils look scruffy, and I’m worried that too much weeding/digging will kill off/dig out the heritage planting and pull out the bulbs that are there ruining it for future years.

How best to deal with/tidy up these borders?

Thanks in advance comrades.