There are a couple of ways in Old School to get polished buttons. The easiest way in my opinion is HAM members. This is so easy, if you pickpocket them for 5 minutes you will have a few. There are a couple of other options if you do not have the thieving. You can also dig in the level 1 or level 3 digsite east of Varrock. Then there also is Ogre coffins or the fishing trawler. This is going to be pretty hard to get them this way. I would strongly advise you to go to the digsite if you do not want to get the thieving level.