Basically, yes you do need both. The nut is there to lock the propeller to stop it unscrewing while the washer butts up against the end of the tube to minimise water entry into the boat.
There are some possible solutions or a combination of them.
It might be possible to get hold of a thinner nut and washer.
Trim the the boss of the propeller by taking the point off to increase the clearance.
If it is just the propeller boss that is interfering with the rudder can you make a small cutout in the rudder to accommodate it?
If the rudder is mounted on the back of the boat is it possible to move it backwards slightly?
Use a smaller propeller which doesn't protrude so far, it will run faster so speed will probably not be much affected on a narrow boat.
Good luck,
Colin