Enter Other Picks From The Draft Board, Not Your Cheatsheet.
Click on any pick to enter the player.
From here, the screen can be 100% keyboard controlled for speed.
You can use the arrow keys on your keyboard to navigate up and down the list, then hit enter to select that player:
Alternatively, start typing a search then hit enter to select:
When the draft rolls back around to your pick, this window will automatically close and you'll be shown your cheatsheet again to make your own pick from.