To get the guts out of your 37 you have to pull the butt stock. It's not a big deal once you have done it a time or two. There is lots of info on the net for this. Under normal usage you should only have to tear it down about every 2 years. I have cleaned several with complete tear downs and did not notice any timing issues when re assembled. One thing you can do without alot of work is unscrew the mag cap all the way off and remove and clean the follower, mag tube inner and spring. My uncle hunted with a 37 for 40 years plus and all the cleaning it got was a wipe with an oily rag at the end of the day. It never failed him.
regards, Darryl