First off, welcome.
Great to see a home build !
22" on a 540 with a straight shaft has potential to go fast, not 70 kmh or anything silly but it will look quick.
You can get away without cooling if you are lightly proped and keep run times down.
I would suggest you get a 35mm prop to start with if the prop is setup for surface drive.
I have a 19" home-brew hydro with a 540 on a x534 prop with no water cooling and it does not get hot, and that thing honks !!
You are on the right track to trial and see if the motor gets hot, short 1 min runs and bring it in to check.
A rough rule of thumb is if you cannot keep your finger on the shaft at the wired end for 5 seconds then it is too hot.
That hatch is going to cause some serious air resistance and looks a bit...........o.k, I'll leave that one for now.

Whereabouts are you in N.Z
I'm on the Shore.

EDIT. ooops i just rechecked the first photo and you have the shaft set for sub drive. Start with a 25-30mm prop.