Well TBH I'd be inclined to question exactly what the customer is looking for if asked for that level of detail, it would seem excessive to need to know everything a pen tester did during a review (and surely a customer that paranoid would have excellent IDS in place and could derive it from that ;) )
That said if you do feel the need, as @abe-miessler says for web application testing, just run all your tests via burp and then provide a burp log. To add to that recommendation I'd suggest using a burp plugin like logger++ which records details of tests performed by the scanner/intruder etc.
If you really want to do this on a network test, then for packet capture I guess you could run tcpdump with a capture filter of only the target network and combine that with bash history to provide a list of commands.
If you want to get a bit fancy and DevOps style you could run all your commands from a Docker container, then provide the output of the
docker logs command as evidence of what commands you've run.