There are mountain passes in the USA higher than 2,800 metres and they don't have warnings and such about driving through them. But it is a risk. Cusco adds 3,000 feet to that. Take it slow, maybe have Diamox handy, or ask your MD and start it prophylactically. Rent an oxygen concentrator, take taxis for a few days vs. hill climbing, rest appropriately.

The pressure altitude in the plane might be close to the same, do you handle that reasonably well on a long flight?

Have a budget allowing escape to a lower city. The OP did not say if it's a connection, a day or a week.