What does ultraviolet light from hot stars in very distant galaxies reaches us in the form of?
Ultraviolet light from distant stars normally arrives as ultraviolet light.
Once a photon of light has been emitted at a particular frequency, the frequency will not change no matter how far the photon travels.
The only way light can change frequency is if it collides with matter. When this happens it is absorbed to put the matter, usually an electron in an atom, into an excited state. When the electron returns to a lower energy state it will emit a photon. The frequency of this photon is entirely governed by the energy gap between the two electron states.
So, ultraviolet light emitted from a distant star will be unchanged when it reaches us unless it interacted with matter. If that happened it will be transformed into a light frequency associated with the composition of the matter it last interacted with.