Be clear.----Does the pump work with a drill ( impeller submerged ) in a bucket ?-----Does the tell tale pee , yes or no ?----Is the motor running hot ?
A light spray of water does not kill an outboard.-----But owner needs to understand what a " light spray " is.-----And owner needs to understand that motor must run for a while to get rid of that water.----Water sitting on bearings is BAD !!
OCboat----Install a new impeller now.-----A 77 does not have a warning horn or a shutdown feature.----It ( and many have ) will run and destroy the cylinder walls !!!!
???----You would have to swap the driveshaft.----OR it would be simple to swap the clutch dog and reverse gear.----But what if there is low oil pressure or shift piston is not moving correctly ???----Your location ?
You need to make sure everything is in order.----One plugged main jet and you could be doing the job over again.----After this epic struggle I doubt you want to do that.----Good luck with it.