welcome here!
i’ll ditto everyone. it is important that they get regular hay (grass hay, but it doesn’t have to be timothy per se). the regular hay has longer strands and that is what they need to keep the gut moving and in good condition. cubed hay can be used as a tasty treat, but should not be used in lieu of real hay. it does not have the same fiber value…
alfalfa hay does taste better to many buns, but it’s important that at this point the bun get weaned off of it. what you can do is feed 90% alfalfa/10% grass hay for a week, then 80% & 20%, 70% & 30%… etc… gradually reduce the amount of alfalfa and increase the grass hay.
if your rabbit is getting alfalfa pellets now, you will also have to wean them off of that and introduce timothy pellets. do it gradually just like with the hay…
what kind of veggies do you feed daily?
you can try to wear a painter’s mask and gloves so you have limited contact with the hay. or is it possible that someone else in your home can be on daily hay duty?