Countries by First Two Letters and Borders in 30 Seconds

This is a set-cover problem, so there's no clever solution (as far as anyone knows). But there are strategies to reduce the problem size:

For example, typing "VA" is never better than typing "IT", because they both cover Vatican City and Italy, but "IT" also covers other countries. Likewise, everything that covers Uruguay also covers Brazil, so you don't need to try to cover Brazil separately.

This allows me to reduce the problem to 55 letter-pairs and 96 countries.

I then try every combination: for every country, I choose a letter-pair that covers the country, and continue until every country is covered or until I've picked 21 letter-pairs; then I backtrack and choose a different letter-pair. This search runs in about 10 minutes on my computer.

It finds several 42-letter solutions, and nothing shorter. One possible 42-letter solution is:

CH CO MO GE GU SA SO TU LA IN AU NO UN BR IS BU DO GA SP ET IT