I don't know of any correlations to physical exercise and chess skill, so I can't speak to walking or swimming.
There's not much that matches chess in regards to tactics but maybe some similarities in games like Go or Amazons.
What will probably give you the best return on your time would be memory enhancement exercises. These come in every style so I would just experiment and see what helps you. Any improvement on how much you can hold in your head will directly improve your chess game.
I also especially enjoy problems where you need to evaluate a board and determine the best move. I try to put time limits on myself to practice how quickly I can analyze a board without missing anything important.