Shroud cleaning?

Id like to clean out my shroud of my Cricket .22 standard.
I can see buildup on the inside edges of the baffles and the holes I drilled in the shroud blow lead dust out and it builds up on the barrel and scope rail.
With all my other supp I soak in mineral spirits then a 50/50 mixture of vinegar and hydrogen peroxide and then dry with comp air.
Since the lead buildup is probably just stuck there and not burnt on could I use just hot water or clean it like any other supp?
Thanks