1. Have you looked into cordless, rechargeable sweepers on amazon ? Bed Bath and Beyond might carry the Shark cordless, rechargeable, dust cup pull-out sweeper. (however they don't make sturdy, easy to push sweepers like they used to, back in 2003, which sucks).
Be on the lookout at thrift stores or at rummage sales, just in case, you can find a sturdy sweeper with a tilt-mode handle that won't easily break. The dust cup pull-out on Shark models works well for picking up small fragments of hay strands! (We sweep every night to keep any chaff or scatters off the carpet and rugs.)
2. Our main go-to for vacuuming for our crew is a Dirt Devil with Filtrete disposable bags. The hose is wide enough to suck up clumps of hay, and fur that is removed from carpet surface or the housing quads with a slicker grooming brush with soft tines.
3. Alternately, a fan-shaped plastic Leaf rake helps to gather scattered hay into a pile - then clumps can be grabbed with hands and put into portable grocery sack for emptying later in a garbage bag. A small leaf/little digger rake can be stored behind a door or in cleaning closet.
Shag carpeting would cause challenges! I relate! // There may be more threads on this topic by using the RO search function.
HTH,