This is their disadvantage. You should leave them on until fully wilted and yellow. Daff leaves can be knotted or tied to make them look neater. Alternatively you could lift them all out and let the leaves die off in storage. It's only for another week or so.
Digging them up from the border is best option in my opinion.
spread the plants out in a sunny position to allow the leaves to wither, before cutting back.
The bulbs can then be stored in a shed or somewhere cool, dark and airy, ready to plant in the Autumn.
digging them up and drying them off or cutting off the leaves will both have the same effect which is to stop the bulbs making resources to flower again next year. If you don’t care that’s fine but id you want them to go from year to year you need to put up with the leaves. What you can do is plant them in pots and plunge the pots in the garden. Once they have flowered, lift the pots and put them out of sight to allow the leaves to die down naturally. Don’t water. Plunge the pots again in the autumn.
Cut off any flower heads after the bulbs have finished flowering. The energy then gets diverted into the bulb for next year. If you dig up be careful not to split the bulbs with the spade. If you leave them in feed the bulbs after pulling the yellow stalks. Best not to tie them.