Do your printer and router support SNMP? I'm not sure how DynDNS works, so in fact if you can ping your network appliances and they support scanning via SNMP, you should be able to inventory them as well.

I am quietly confident that at least the printer should support SNMP. It is currently set up with a wireless connection to the router.
DynDNS gives a permanent external IP address like 220.232.whatever.whatever to a particular machine, regardless that it does not have a static IP with the telco. I can scan the IP address allocated by DynDNS and get to the Mac, through it's router, over the internet. The internal network with the Mac, printer, and router on it, is the usual type 192.168.whatever.whatever. which I cannot access from here as it would just scan my local network. I am guessing I am stuck.

I am talking to my test lab about this now. I'll update you soon.

We did some tests with Hamachi and dynDNS, and it seems like dynDNS is not the best solution here. The most usable ideas would be to either VPN into the target network and scan from there, or configure port forwarding so you can access those printer and router directly. If any of these options sound feasible, we'll be able to provide more details.

Thanks Jeff, I will try the port forwarding option next.