I suggest a DCO (Direct Contact Overlay) mount using at least one 1/4" layer of needle-punched polyester batting over a sturdy, decorative backing board; perhaps fabric covered. The batting would compress under slight pressure, and it has a texture that might tend to 'grab' the fabric on the back of the map, making other attachment provisions unnecessary. Use abrasion resistant, 98% UV-filtering acrylic, such as AR-OP-3 orr, if the customer wants the best possible view of the map, use optically coated Museum Optium Acrylic.
Yes, it is OK to have the abrasion-resistant acrylic in direct contact with a flat-textured paper item, but never use glass in direct contact. The acrylic has better thermal properties and would not easily condense moisture, unlike glass, which is a poor insulator and readily condenses moisture. Proper handling, and therefore customer education, is important with any DCO-mounted framing. For more on this, search the archives for "DCO", "Direct Contact Overlay", and "Dew Point".
If hinging is necessary, I would probably attach lightweight fabric hinges using Lascaux 360, a conservation-grade, reversible, heat-activatable contact cement.