Every tool on this site runs inside your browser — that is the whole point, and it is the reason none of your files are ever uploaded. There is no server-side version to fall back to, so with JavaScript switched off there is nothing here to show you.
Turning it back on for this domain is enough. The site still makes no network request with your files in it.
Draw your signature, put it where it belongs, and download the signed file.
pdf.js + pdf-lib · idea from Stirling-PDF