I was taking a look around at some Romhacking tools and interestingly enough I stumbled across this editor:
http://www.romhacking.net/utilities/564/So putting in the work there it would be possible to edit the tiles and enemies to resemble what is in Belmonts Revenge might be accomplished using that. Now for the music:
http://www.romhacking.net/documents/634/That of course will be tougher to get along with editing the actual Megaman sprites to resemble Christopher Belmont. The way to do this would be to use Tile Molester, find each Megaman sprite and edit it:
http://www.romhacking.net/utilities/109/If you open the Megaman 4 ROM you can see Megaman's face and body are both separate. What really would need to be done to resemble a Castlevania character such as Christopher Belmont would be for the head and body to be more proportional. I think carefully this could be done.
The final part I don't know is doable and would be very hard if it is. See Megaman doesn't use a Melee weapon. He uses a gun and every weapon he obtains in Megaman 4 with the exception of Toad Man's Rain Flush and Bright Man's Time Stopper is a gun. The only way a whip could become the weapon is to somehow create a Melee Weapon out of Ring Man's Boomerangish weapon using ASM and make the collision right. This would also have to be the main weapon. This is the part that's the trickiest.
Some other issues include: No candles, No Time Meter, and how the bosses will function.
Anyways that's a basic blueprint I have for it. I don't know if I could do it or would do it but its an idea nonetheless.