I'm confusedOoooooooh , don't do it !
My preference is a stainless steel, straight shank, oval head screw. This style is called a sheet metal screw.If the removal of the screws caused the block to drop into the hull you won't have any way to get backing for the handle except to get into the hull. If the wood block is still behind the deck you can get new stainless screws for the new handle. I don't know the screw size.
I'm confused, why not re-attach a bow handle?
My preference is a stainless steel, straight shank, oval head screw. This style is called a sheet metal screw.
I begin by cleaning the screw holes with something such as a pipe cleaner. I peer into the hole using a light and even probe with a wire to see if the backing block is still firmly attached and not rotting.
If the block is there and in good shape, I fill the holes with epoxy, churning it with a bit of wire or a toothpick while I drizzle it in to be sure it flows to the bottom of the hole and there's no trapped air.
Once the epoxy has set I re-drill the holes to the proper drill size to match the screws I chose. Take the handle with you when you shop screws to match the screw head to the handle's counter-sunk holes..., that will likely get you a shank that's reasonable for the job.
The backing block is around 3/4" thick so 1-1/4 shank length would be about max you need. [ Handle + Deck + Block ]
If you discover the backing block has fallen or rotted away, post a new question for hints on dealing with that scenario.
"Can anybody help me with what kind of screws I need and how it is secured in a stable fashion to the dick?"
Ooooooooh , don't do it !
Before you screw the handle back down, apply:
3M 5200 Marine Adhesive Sealant
to the base of the handle, it will glue the handle to the deck.
I'll second that and just add, a thin film of marine silicone caulk or equivalent doesn't hurt to keep water from seeping in and promoting backing block rot. However, if you epoxy and re-drill the holes the backing blocks should already be sealed. If you want to glue down the handle permanently why not just epoxy it to the deck (not recommended)I strongly recommend that you do not use 3m 5200. 5200 is such a strong adhesive you will never be able to get the handle off in the future if you need to
I'll second that and just add, a thin film of marine silicone caulk or equivalent doesn't hurt to keep water from seeping in and promoting backing block rot. However, if you epoxy and re-drill the holes the backing blocks should already be sealed. If you want to glue down the handle permanently why not just epoxy it to the deck (not recommended)