For openers, President can’t levy a tax. The Congress must do that.
Secondly, any one with money and an internet connection can easily transfer money to an office in Mexico that gives it to whom ever it is being sent. The Two parties settleup periodically by official bank transfer.
In days not very long past, Mexicans could purchase mexian lottery tickets in their local bean house via the restraunt fax to a contact in Mexico city. I would presume that is via the internet now.
Thirdly, banks are in the business of international funds wire transfer. Any such method you propose would be discrimatory if not applied to banks.
Trump has the bully pulpit and can certainly propose legislation.
And he can administratively levy tariffs and fees and such a levy could be crafted via graduated schedules to allow large transfers.
It is complex but it could be done even without Congress but as we learned administrative solutions can be short-term.
Better to sell Congress. They can tax retail then they can tax retail transfers. So long as EVERYONE doing the same transaction is taxed the same I am sure it could pass muster.