Oh man I feel you! The spraying is nuts sometimes. As early as it seems, he is right on time, as puberty can start as early as 12 weeks.
I think a good temporary solution would be to set up an exercise pen (or two) linked up to his hutch that is lined with a waterproof flooring, and even some blankets, towels, or shower curtains hung on the pen walls. That way he can get some exercise but your home will be protected. He definitely does need exercise while waiting for his neuter.
Good flooring options are a tarp or plastic sheet with blankets on top (cheapest option), or they also have waterproof dog blankets and “welping mats” that work well with buns, but those are more expensive.
There is a chance he could settle down a bit over the next few weeks (even neutered buns will sometimes act extra hormonal in the spring time), but the behaviors won’t likely go away completely until a few weeks after his neuter.
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The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.