I would agree with Aubergine get the proper tool. Amazon is a place for cheap junk delivered way too fast. For tools and bike parts your local shop is a way better option and if not then there are online bike shops that are linked to brick and mortars or if you really don't want to support local business at all there are bigger bike shops that are online only and make loads of money sure not the same as some of these third party places but still way more than the smaller local shops who would appreciate your business.

I would look at a fixed cup tool from J.A. Stein and then the proper wrench from Park Tool or Pedro's and problem solved. Or if you don't want to buy quality tools just have your local shop handle it and spend more time riding.