I have something similar. Someone asked for a signed PDF. I digitally signed it and sent it to them. They said it has to be scanned. So I did some image magic fu to it to rotate it and make it look crappy. Then they accepted it.

My goto technique: apply signature stamp. Flatten. Change blend mode to multiply. Convert page to image. Rotate image by 0.5 deg. Paste scanned page on tape. Flatten. Change blend mode of image to burn or multiply. Convert to image.

The only tell tale sign is that the text still has this aliasing like texture that doesn’t happen in real scanned pages.