Can I install a switch between two GFCI outlets so that only one can be used at a time?
This way of doing it is a little risky, because some GFCIs don't like to have their power interrupted on a regular basis. 

A GFCI+receptacle combo device creates a zone of protection in its own sockets and anything downline that is attached to the LOAD terminals.  Hot and neutral must feed symmetrically from LOAD.  Ground bypasses the GFCI entirely (and that's important for it to work). 

I'm not fond of your arrangement because aside from severing power to GFCIs, it violates a few of my "rules": 


Don't put two GFCI devices on the same circuit
Don't put a GFCI device outdoors


So I would recommend installing one GFCI device that is upstream of the switch.  Then use the output of the GFCI, via the 3-way, to feed two plain receptacles. 

I would also use a 20A-grade 3-way.  This won't cost $2. 



Here I use brown/gray for hot/neutral in the protected zone, then I switch back to Romex colors just because I didn't want to redraw all that.