First thing I do when I get out of the truck is scan 360 degrees thoroughly and see if there is already a coyote/s there. If so I'll set up the gun right there and kill it, then walk in and call. I've killed several this way. If it's clear, then I'm not worried about the red light for walking in. I'm more worried about stumbling or falling from an obstacle I can't see.
As far as splash, our scanners are helmet mounted and splash is minimal. When I tip it up to get in the scope I make sure to point it to the ground. I keep my rifle at a slight angle or stand beside it instead of behind it, until I'm ready to get in the scope so the light is shining into space and not reflecting off me. My scope has a rubber eyecup on the eyepiece that I rest my eye on when in the scope.
Just like in daytime hunting, if you can wait to make these transitions while the coyote is moving and not standing looking your way the chances of them noticing you are greatly reduced.