How do I transfer Preview's PDF signature to another computer?

Why don't you just copy and paste it into an email and then mail it to yourself.

 

When you copy and paste it, it is just a .tiff file.
The email method was just a easy way to get it to another computer, you could just as easily use airdrop, usb flash drive, network transfer etc.

Once it's on the other computer, you can insert it into any document as often as you like.