When the ultraviolet light from hot stars in very distant galaxies finally reaches us, it arrives at Earth in what form?
Ultraviolet light from distant objects arrives as the same form of ultraviolet light.
Light travelling through space for any distance remains unchanged.
So, ultraviolet light emitted from a distant galaxy will still be ultraviolet light at the same frequency when it arrives at Earth.
This assumes that the light wasn't absorbed by an atom on its journey. If it was it would have been absorbed by an electron and re-emitted at the electron's transition frequency.