I think the Alchemy Whip is strong enough to kill almost anything. But Walter was protected by the Ebony Stone, which only the Vampire Killer could destroy.
Mathias was transformed into a vampire by the Crimson Stone, and given power by it, but I don't think that stone offered him the protection that the Ebony Stone did for Walter. Since Dracula isn't protected the way Walter was, I think any powerful magic or weapon would be effective in killing him. Obviously this pertains to the Vampire Killer, but I think it also pertains to other magical weapons like the Hunter Whip, which I've always seen as another full formed Alchemy Whip that wasn't turned into a Vampire Killer.
I also think that killing Dracula isn't just about the weapon. No matter what magical sword, spear, whip, etc. one uses, every warrior that has faced and killed Dracula also has incredible amounts of fortitude. Not only did every warrior have to make it to Dracula, they also had to fight him in his many forms. And with a few exceptions, most of them did it alone. Not just anyone can do that, or Joe the peasant farmer would just take care of it with his pitchfork every time Castlevania rises out of the mists.
I think when it comes to killing Dracula, the warrior is just as important, or even more important, than the weapon they use.