"Raindrops keep falling on my head" never did it for me. "Spent brass keeps falling on my hat" does. Still waiting for the recording to come out. +1 to jimboborg and Kent Shootwell.
After CAS practice with someone else's Winchester '73, I bought a pre-buyout Marlin '94, which I love shooting. But, alas, the minor thump of brass on the brim no longer happens. So +1 to Drydock, too. Your choices are up (top eject Winchester) and out (side eject Marlin). For anything else, you could contact those guys at Red Jacket if you have the money. But it wouldn't pass NCOWS or SASS since it wouldn't be pre 1899. If you really don't want your hat touched, go Marlin. (pre-buyout if you can find it.)