I have an photo of a handwritten signature that I use in Adobe. They do a pretty good job of extracting the signature contours from the photo. I've also seen a (much crappier) version of this on my mobile banking app, for processing photos of checks. They basically just blow up the contrast until only the blackest part of the image remains. It looks awful, but it might be a good place to iterate from. If you implement something more sophisticated, it definitely makes sense to save it on the backend so you don't have to redo the (possibly expensive/slow) image processing operation every time.

A signature pad could work too; I think HelloSign has something like that. But it's not a great solution if you don't have a tablet, since it's really hard to draw a proper signature with a mouse. Honestly, even just adding a "handwriting font" might be good enough for most circumstances. Most of the document signing services provide this, and it could be implemented very quickly with minimal changes to your API.

If I were you, I would probably start with a handwriting font, and add hand-drawn signature support afterward. I would also look into what the law says about this sort of thing. I know that services like HelloSign require that you authorize them to use your signature in a legally-binding manner. But I don't know if that regulation would apply to your service, since your service is a lot more bare-bones. For example, you don't store the PDFs indefinitely, and you don't coordinate any sort of multi-party signature operation; that all happens out-of-band. So you might be in the clear.