How do I sign a PDF document without a printer?

Open the pdf with Preview and use the markup tools to create a signature and sign the document. Save that doc and ship it back to the sender.

Fill out and sign PDF forms in Preview on Mac - Apple Support

If your doc requires a notary signature, that's a different story. A hard copy would likely be necessary. In that case perhaps the services of a local printing service such as a Staples or Office Max type business.

A second look at your post and I realized that while you're not home maybe you are also without your computer.

If you have your iPhone then you can sign the pdf with that device by using Markup tools on the pdf.

Apple provides guidance for using Markup and adding a signature here:

Fill out forms, sign documents, and create signatures on iPhone - Apple Support

If you have an iPad, I believe the process is similar on that device.

You can create a signature in Preview.

Open a PDF document (any PDF). Do Tools > Annotate > Signature > Manage Signatures > Create Signature > Camera. Write your signature using black ink on a piece of white paper. Hold it up to the camera until Preview senses the signature. Click Done. (If you have a trackpad you can also do this with the trackpad.)

You can then add the signature to any PDF document by doing Annotate > Signature > (select signature). It will add what looks like a text box containing your signature. You can move/place it anywhere in your PDF.