There are a few types of inertia seatbelt locking mechanisms, you cannot be sure it would work or not without understanding how they work or at least testing them in situ, i.e. by driving down a road wearing it then braking hard. Most work two ways.
1/ through the inertia of a lump of metal, that in an accident or under braking either slips, slides or swings and that motion moves another part of the mechanism that then locks the reel.
2/ the other is where it relies on the speed at which the reel is turned as the belt is pulled on rapidly causing a weight to spin outward due to centrifugal force, this then acts like in 1/ contacting a piece of the mechanism and moving it so that it in turn locks the reel. This method is slower and allows the person to move further before restraint takes place.
I cannot see how the two belt mechanisms themselves can be handed, as they should work no matter in what direction the car moves suddenly, i.e. the inertia should act in any direction or plane. A seat belt still works if you are hit from behind or the side, or indeed if the car rolls over. Not just from the front.
Here is a description of a universal seat belt you could buy cheaply if you wanted to fit one to a classic or a kit car, you will note that it says it can be fitted to either side and front or rear.
So why not simply remove the driver's side belt, replace it with the passenger side one, if the mountings will allow you to, then go for a drive and, where safe, brake hard and see if it holds you? Either it will work or it won't.