I deadhead the blooms at any time I want but that means I leave the task to Mother Nature. ;o) To remove spent blooms, you can cut the peduncle, the string that connects the bloom to the stem. I like to see the color changes but if you do not, you can deadhead once the sepals change from white to shades of green. Or when the bloom finally turns brown.
Then, as my summer temperatures arrive, I prune any stems that have not leafed out and remain lifeless. You can confirm that they are dead by carefully scratching the bark to se if you see green or not.
Lastly, throughout the rest of the growing season, I monitor stems that bend/flop in order to see which ones straighten out by themselves and which ones do not. Then I prune the ones that remain bent either partially or all the way down.
I prefer to avoid pruning Annabelle stems as older stems are woodier, stronger and flop less than new, green, pliable stems. But... I understand having to prune most or all stems if the plant is in a location where it gets dumped with snow often and the stems get broken or bent by the weight of the snow.