Getting the card with your wife as guarantor or cosigner will not help you build any credit history in Taiwan. All the credit reporting and risk goes directly to your guarantor. If you really don’t care about this, then getting her to cosign for you will work, or you can just ask your wife to add you as secondary to her card (fu ka)
I absolutely refuse to get anyone to cosign for me as it is very discriminating policy and I will not support banks taking risk free loans but charging me outrageous interest rates. If this is not a concern for you, you can try FarEastern bank as I know for a fact they issue cards to foreigners. They require your financial bank info and your cosigners eg bank deposit book copies, and then they issue the card if you qualify. Taixin will as well.
If you want a card in your own name with no guarantor, it takes a bit of work. If you tell me what bank your salary goes into , I can likely tell you if the bank will issue foreigners a credit card or will make exception to do so. PM me the info if you don`t want to share it here or you can just post here.