I can assure you, with a great deal of confidence and a wide representative sample to choose from, that lousy handwriting is a) not unusual b) not nearly as bad as the writer thinks it is, and c) still welcome. Typed letters are also welcome. I get a number of those in which the only time a pen touches the paper is to sign the sheet. I still enjoy them.
The purpose of the Challenge isn’t to avoid the computer at all costs. It’s to slow down and give yourself permission to think about just one person at a time. Also, to hopefully seed your mailbox so you get mail in return, but that’s a bonus.