This can be, and is, done quite often. The usual reason for a kilt having the apron open on the left is because it was made for a women. There is a school of thought that if it is made for a woman it should be fastened opposite of something made for a man.

Please don't tell female members of pipe bands this though, they wear the exact same kilts as the guys do.

The problem you will face is dealing with the strap hole if there is one. The quick fix is to sew the strap hole closed and when installing the new strap on the left side to put it inside the kilt.

Can you tell us if the pleats are opposite too? Normally the pleats would face toward the wearers right side. We have at least two men here who prefer to make their kilts with left facing pleats. They both live in N. America and find getting into a car with left facing pleats much easier.

If you understand the internal construction of a kilt you should have no problem reversing the apron. If not any kiltmaker could do it for you. I will caution however, this would take at least a few hours to complete and the labor rate could exceed what you paid for this kilt.