What if the whip is just the handle through which the Belmont wielding it channels his power?
That would explain how Simon can change the tip; He simply buys a new one to attach to the handle.
Juste was shown to be able to change the tip too (but in his case, it was the very tip of the chain). However, he also had a myriad of stones (Red, Blue, Yellow, Green) that added a number of elemental effects to the whip itself. It may be the case that the handle has a slot for these stones to be placed on.
Rinaldo may have enchanted only the handle, and it could be made of metal, as it's explicitly said that he used alchemy to do it, and metals are generally associated with alchemy. If the Vampire Killer is only the handle, then it also explains how Leon can enchant the body of the whip with new "whip" items. He's simply changing the tips.
Also, there is the fact that the tip can get rusty (in case of metal), or withered or shredded (in case of leather). It would be wiser if the tip can be replaced as time goes by. Unless it's magic. Then nothing can be done and we can say anything, including "it shapeshifts" xD
I once tried remaking Simon's Quest, and in the story, there was only one person who sold you "new whips". He was a special blacksmith, and required you do gather materials from monsters (explaining why Simon has to kill them, and the drop items) which included bones, hides, skin, blood, herbs, pieces of armor, and he could use alchemy to infuse it all on the whip itself, enhancing it.