The only rear shifting mech with a trim function is going to be down tube friction shifters. (Ok, I guess they could be mounted on the bar end, too).

Front shifting often has trim positions, but it's really easy to set up a front derailleur to shift from big to small and back down again while completely failing to tune it for the trim positions. For the large ring, the trim position is used for when you are in the largest 3 or 4 cogs on the cassette as the chain will sometimes rubs on the inside plate of the FD. Sometimes bikes work out and you can get no rub in the big/small combo and virtually no rub on the big/big combo where the trim would be needed (but this is generally a bad idea for other reasons, known as cross chaining).

If the rear cassette is making noise and you think the chain is not lined up properly, then the rear derailleur needs to be tuned and/or the derailleur hanger needs to be straightened. A properly tuned index shifting bike should not need trim on the rear.