Is the interior finished? Is there an accessible crawl and/or attic space? Protecting existing non grounded circuits with a GFCI is no longer code compliant. If you change out a 2 wire receptacle from 2 wire to 3 wire grounding you have to run an Equipment Grounding Conductor to one of several places the US National Electric Code (NEC) now allows. Even the GFCI, unless you use a blank face model in a double gang box, changes that receptacle to 3 wire thus invoking the requirement for an EGC to that box.
If they really want maximum safety give them a price on rewiring it. If there are baseboards you can remove them, cut out the portion of the wall sheathing that is behind the baseboard while leaving a 1/2 inch of finish at the bottom edge so all of its bottom edge will be below the top of the baseboard when you reinstall it, and drill holes above the top of the baseboard through the studs by angling the body of a right angle drill upwards above the bottom of the wall sheathing.
[If the interior wall sheathing turns out to be 1/4 inch wood paneling, as that of many summer cottages are, do them a big favor and convince them to have it removed. When that thin siding is mounted directly on the wood framing the rate of fire spread over the surface is faster than a healthy man can run. Ignition to flashover can take as little as 20 minutes. That is when the entire remaining contents of the room burst into flames simultaneously. The compartment is then said to be "fully involved" in fire. When firefighters hold a structure fire to the compartment of origin it is said they made a "Good Stop." once the compartment of origin flashes over it will force fire out the door in imitation of a blowtorch. They would be lucky to save the remainder of the house.]
Once you run the new cable then install a backing board to the baseboards back side to keep the same reveal on the baseboard top and put them back in with screws. Strips of CD plywood or even oriented strand or particle board work well for this and give you a wide range of thicknesses to choose from The advantage of using a spacing plank behind the baseboard is that you can attach the baseboard to the spacing plank and fasten them both to the wall framing with the same screws. If you countersink the screws back of the front of the baseboard you can then cover the screw heads with the push in plastic plugs which most closely match the baseboards. Cables can also be run behind door and window trim without a huge amount of trouble. All it takes is a somewhat thick piece of roof flashing to guard the cable from nails and screws. I've had inspectors except doubled up flashing to get the required thickness.
Tom Horne