I was unaware that keyloggers can take screenshots! Yikes!
I and family travel to Ireland every year. I do not take my laptop, but while there I do occasionally use the public computers at the B&B's. I never log in to banking/credit card/email websites from those computers, but I had the thought that one could simply put usernames and passwords in a text file and on a memory stick, plug the stick into the computer, and swipe/paste that data to log in to sensitive areas. Using that technique you would never type your actual passwords, but screenshots would remain a risk!
Sure, that poses the risk of the memory stick being stolen, but there are other solutions to that as well, such as "coding" the passwords, then uncoding them later without having to type in the entire PW.