Without that contract, they have no rights at all. So what's the point?
By default, the only person with rights to a copyrighted work is the copyright holder. Everyone besides the copyright holder has no intellectual rights to that intellectual property. The copyright holder can give/sell/license off rights as they see fit, but by default, no one else has any rights to your works.
You're not responsible for proving that they DON'T have rights... THEY are responsible for proving that they DO have rights. Make sense? The burden of proof is on their shoulders.
The "contract" your talking about is only for THEM to prove they have rights. It serves no purpose/has no benefit to you as the beat maker UNLESS you are asking for royalties or you have some sort of other arrangement made for the future (i.e. the client will buy 10 beats a month for $100; or something like that). Therefore, having YOUR signature on the "contract" is important, but having the clients doesn't matter.
Having a client sign for the rights you've given them is like having a customer at a local store sign their own copy of their receipt. Like, you CAN sign your own receipt if you really want to, but there's no point since your receipt is for your own protection, not the store's. When you go to return an item to Walmart for example, they don't look for your signature on your receipt.
The question is, are you asking for royalties? If you're not, you don't need their signature.