This question is not pertaining to the development. It is rather deployment question.

My client has bought another domain name and his provider is not sharing its user id and password. they asked me to share my name server. Is it safe to share my hosting account name server so that he can propagate the domain name to my hosting account.

For support I often have to know this to test the name server and then compare results to other name servers.

In this case this information is needed to propagate details. So another good reason to share.

Now how do you explain to folk that I can't exploit your PC's IP address of

Your name server are available on the internet anyway. If you are on a system with whois installed (rwhois) then you can enter

whois <domainname>

And you get all of the information about that domain including who owns it, the registrar, and what the primary name servers are. You can get the same information from any of the whois sites out on the internet.