I think you should let him handle it. Tell him you have plans. As long as you fix it for him (keeping son 'safe'), you're also preventing him from being a real parent.
Has he ever put his son at risk? Would he not know how to pick a sitter? Do you truly feel your son would be unsafe? Would he be out in traffic or with drunk people?
Many fathers step back from parenting because they feel they are supervised and criticised by the mothers. It's a negative cycle.
M 16 yrs, WH62, P54 3 adult blended kids EA 11/13, BD1 6/14 PA fall 14, BD2 2/15 Piecing 2015, BD3 12/15 Separated 4/16 WH moved OW in 5/16 Divorced 6/15/17