I guess it depends a little on how comfortable the owner is with having someone else tweaking the system. Also, it depends on if you have an AM4 compatible cooler.
Certainly, you could buy a 1600, use the stock cooler, OC to 3.7 GHZ, buy some RAM, read a bit to see what kind of compatibility/speed you could get out of it, set both the CPU and memory in BIOS and the owner would probably never be the wiser.
Alternatively you could do what Topweasel suggests (and it's probably a better choice generally), and get a 1600X a cooler from somewhere, and RAM you don't have to fiddle with (2133 RAM is about $100 for 2x8 GB). Installing my 1700 and getting it to work at stock clocks and JEDEC standard 2133 RAM was very easy. There is nothing remotely unstable about the system. The only difficulty was in getting the RAM about 2133 and I had to settle at 2933 instead of 3200. But even then it was a matter of the overclock RAM profile not working, the system cycling for a bit before rebooting, and then manually entering 2933 and the memory timings in BIOS. It took no more than five minutes.
The closest person I know who is clueless about PCs but I would build a PC for is my wife. In her case I just buy and build what I want and tell her what I did. Usually it involves her complaining she's getting leftovers from when I upgrade.