Yes.
Copy B of a 1099 form can be printed on plain paper with black ink. The payer could hand-write all of Copy B and send that to the recipient.
Copy A is sent to the IRS on red-ink forms. In the publication General Instructions for Certain Information Returns, it is written
“Although handwritten forms are acceptable, they must be completely legible and accurate to avoid processing errors.”
You can fill-out Copy A by hand with black ink and block print (not cursive) and mail in. Do not enter “none” or “n/a” for a box that has no money value. Instead leave that box blank.