A third alternative (I think) is the enclave of Ceuta, just across the straits from Gibraltar, it's notionally Spanish, but like the Canary Islands, is not part of Schengen/EU; again, you'd do it in 24 hours from Huelva.
"The Azores and Madeira, as part of Portugal, and the Canary Islands and Balearic Islands, as part of Spain, are included in the Schengen area. Ceuta and Melilla – Spain’s autonomous cities in northern Africa – are a special case: they are part of the Schengen area, but border control is still in force there. France’s overseas possessions, on the other hand, are considered to be outside of the area."
I believe the information on this site will be very useful to the OP.