Ladybird68:

Don't visit forum, check message or respond to in games messages when going for the record,
Gammon games with autopass and the right opponents can do wonders!
Checkers has a low click per move ratio if you click the piece with one legal move.
Double every gammon game with the cube at the start it stops you getting asked to roll the dice each time.
Ludo is naturally a good candidate.
Mancala as a silly game that is won for the starter, so no need to be concerned if you lose.
Horde chess another unbalanced game that doesn't need much thinking.
Pahtum another game needs little thinking!
Any game that is hopelessly lost, politeness would say resign, but these are perfect for the goal of most move in a day and a bonus you get to really annoy your opponent should they timeout! If achievement for most moves exist sthen not resigning is understandable that they will be used because they can't messed up so no disappointment for losing a game that is lost.
Although there is someone who plays and has all the most move achievement always plays until mate, is just insulting.
Dice poker if you preroll your dice and don't move, instead save the games until you are making your attempt and you have a move that can be made quickly.
Don't mind that stupid errors will be made, at the speed necessary to complete 10,000moves!
If you have a rating you care about don't use that as a game to attempt the record with!

thisbeme:You lost me with this low click per move talk. I was unaware of any esoteric features to my checkers games.

Purple:
Pedestrian's post below explains the principle very nicely.
Draughts often can allow a move to be completed in 2 clicks, 1 click to move and 1 for the confirmation "move" button. If a piece only has one possible move then clicking on that piece will automatically move it to the only possible square.

thisbeme: Good God. You would need the laziest fingers on the planet to fret about that. lol

Purple: It wouldn't matter much in normal games, but if you try to make 14000 moves in day, it makes a significant difference.

Aganju: An admirable goal..I guess.