As long as it's not for commercial work or purposes, it really doesn't matter.
This just loops back around to pirated music/software. If you don't use it to make money, they have no case against you.
If your website has a payment system or a donation or something, I also think you're fine, because you're not distributing the work, and technically you're not violating DMCA, because the edited (remixed) work isn't being sold, and is available without paying..
I'd quote DMCA but I can't find this quarter's version.
EDIT: To go with what lemon-tree said about being contacted by the original artist:
Under DMCA and the US Copyright Law, if the owner files a Cease and Desist without notifying you or asking you to take down said work, you can countersue because of the subsection of the DMCA about "Failure to Notify"