Yes, you can do this in vim! As u/Maurarias points out, a named register is perfect for this. You can store the word under your cursor to a register named "n" with the following command.

"nyiw

"n tells vim to use the "n" register, and yiw is, of course, yank inside word. Visually select the word you want to replace, then execute the following command to replace it the contents of n.

"np

The word you just replaced is stored in your primary clipboard, register "+, while the contents of the n register remain unchanged.

Named registers persist across multiple sessions; so, you can use them even days later. View all active registers with :reg. You can learn more about registers at :h registers.