Hi. If you look at the signature on the Emancipation Proclamation, Lincoln's signature does bear some evidence of shaking and unevenness. This is likely not due to the paper, since the text and the signatures of others (William H. Seward) do not have the same quality of unevenness on the page. This is only a partial answer, since I do not know about the reason for the shaking, I can just assert as someone with expertise in signatures that it does look shaky.