hmmmm...that all looks pretty tight. There is usually a lock nut between the ship and the screw and this creates some play. But that becomes problematic because the end of the screw already hits the rudder.

As Wolle says you usually have a nut locked against the prop to stop the prop loosening and to provide free play but space is tight.

The shaft looks to be small diameter so might be relying on the rudder post for some support though I guess unlikely - probably just to copy full-size.

Options are;
To remove the cap and fit a lock nut.
File the end of the prop down and fit a thin locknut.
Drill and tap the prop for a grub screw.

You could use Locktite but given the access to the prop you will have difficulty in diassembling it in the future if needed.

Whatever you do you need to remove the prop so that you can assess the situation clearly.

Chris is right; you absolutely need to remove the prop to see how it is currently assembled. Given the configuration that is not going to be easy.
The prop looks to be right- handed. Is it? If so a thrust washer on the shaft between the keel & prop hub will prevent tightening when underway. It doesn’t have to be very thick. Then use Locktite and use a thinner cap nut on the aft end of the shaft so that it is not touching the rudder post. Having it bear on the post as it does now does nothing structurally. Any aft movement of the shaft can be prevented using a thrust washer at the juncture of the coupling & shaft log. That could help create a bit of clearance between the shaft & rudder post. Locktite or not prop removal will be difficult as built. But if set up well removal should seldom be required
This is merely how I set mine up. Undoubtedly there are other ways that folks use that might be better.

For what it’s worth another thought just occurred to me. Given the shaft/prop/rudder post configuration the intent must be for the prop be unscrewed & the shaft removed from the motor end. Is that possible?

In answer to. Your question yes it is

That’s a good thing.👍 At least the prop is trying to tighten with the hull moving forward. A left hand prop would be attempting loosen. Is it possible to remove the shaft from the motor end?
BTW, the blue Locktite can be removed without applying heat like the red formulation.

If at all possible, even though the Prop may be threaded onto your shaft, Yesvyou should havevz lock nut on the shaft.
If your prop is not threaded you should have a keyed 'Drive Dog collar ahead of the prop and have your Propeller boss, slotted to match the Drive Dog Collar, again with a Lock Nut to hold the prop secure.

the problem is it tightens and then locks the motor as for a lock nut on the other end that stop it moving out not in

The other thing is you could try is to loosen the shaft where it goes into the motor connector (some photos inside the hull would be useful) and then screw the shaft into the prop until the prop comes up against the plain/unthreaded part of the shaft which will stop the prop tightening any further when driving the boat. This assumes that the threaded section of the shaft isn't far ahead of the prop though as otherwise you may not have enough leeway at the motor end.

Failing that you are going to have to take the prop shaft out to see exactly what the situation is and which other option would be best.

My humble opinion on this propeller problem is, the prop is to large for the recess it is housed in. one doesn't normally fit a prop which leaves hardly any clearance room. Also, I should like to add that the rudder looks nice but is far to small to be affective and responsive, especially considering the oversized propeller. For the record I have been designing and building model boats for the last FIFTY years.

Having just given you my opinion on your prop shaft problem I thought I should back it up with the following photo, it might not look very pretty but it will be both effective and manoeuvrable, hopefully and as it turns to ninety degrees it will act as a brake. Regards. Gary.

If you would care to enlarge the photo will find a grub-screw through the prop and into the prop shaft, as well as the vice jaw marks on the rudder brass sheet. Regards. Gary.

Again, to more or less echo what Chris suggested, take the prop off the shaft. Try disconnecting the shaft from the motor, remove the motor, slide the shaft forward to remove it. Take photos, before & after. The suggestions will be more meaningful & you will get a complete view of what you are faced with.

Is there a cap soldered on the rudder? See circle ⭕️ in photo.

Am I seeing a pin in the rudder square post?

its in a hole in the rudder posythe cap unscrews from the end of the shaft and the tapered end of the shaft

To me that is a system designed to fail; a prop screwed onto the drive shaft on one end & screwed into a fixed object ( the rudder post) on the other. As an experiment I suggest you remove the shaft to rudder post fitting and run the motor to see if the shaft screws farther into the prop & binds the motor. All on the bench of course.
Results should give clue(s) about next steps.

as was suggested ive threaded the end cap and locked the prop to it and wallah one locked prop we hope seems to work

Glad you’ve solved the problem. Now we’re ready to see some in-water photos.👍
BTW, I would also put one drop of blue Locktite on the shaft. Once, I neglected to do that & lost a R.H. prop while backing down even though the prop was tightly screwed to the shaft. Duhh!