1) Is it our responsibility to call the customer service to find out if shoes made in non-Muslim countries are made out of 100% real leather, artificial leather, or a combination of both and other materials (i.e., for the purposes of purity)?
2) If I know the shoes are made out of 100% real leather, would that be najis? If yes, then what is the process to keep our body pure when we touch it with dry hands and with wet hands? What if it is made out of real and artificial leather and other materials, would that be najis?
1) If you are not sure whether the dress shoes are made out of natural leather or not, you can treat them as pure, and you do not have to investigate.
2) If the shoes are made out of natural leather or a mix of natural and artificial parts, and there is no reasonable probability that it is from an animal slaughtered according to Islamic laws, then you must treat it as impure (najis). However, it will not make other things, like your skin, impure unless there is contact with moisture, and when in doubt, you do not need to check.