My limited experience is that birds will readily abandon a part built nest
but once they've started sitting, are remarkably tolerant of disturbance.
Providing they don't feel physically threatened (so do be gentle and
careful, especially where those cut off branches are falling) they will sit
tight until the disturbance passes.

Even if you frighten her off, work fast, go away and she will probably
return and continue sitting. Obviously if you leave the eggs too long, they
will cool and die. Wrens eggs are also small so they'll cool fast so you
may prefer to stop for a while to allow her to return and settle again.

Paul DS.