I'm going to take a stab at this as well, even though I'm not fully sure I understand it.
First off, I've never heard of a registrar asking for zone files. Ever. This seems pointless and needlessly complicated. I'm not an expert in how domains "work" as such, but I was always under the impression that the host created the zone files themselves, not the registrar.
A registrar transfer is merely a process by which a new registrar takes over the domain registration itself. It has nothing to do with zone files or anything like that. All other information should be left intact, unless there's a reason to change it...in which case, you change that information AFTER the transfer has taken place.
Next thing: telling where a site is hosted from the WHOIS. Yes, it is possible, but it depends on how the nameservers of your host are configured. Some hosts offer what is referred to as "anonymous DNS", or two nameservers that don't directly reference your host.
e.g. Hostcompany.com could use ns1.privatedns.com and ns2.privatedns.com for their name servers. A WHOIS lookup on privatedns.com might reveal something like "Private DNS, LLC."
It sounds like, and I'm not sure on this, that what your registrar wants to do is to set up a domain forward to the existing host. If that's the case, this will accomplish NOTHING and Christian_SEO is right...this is a beginner move at best.
You should be able to leave the WHOIS information intact other than the registrar. Any registrar that requires this or anything else to be changed on transfer...well, they suck.
www.godaddy.com (there's an okay one.)
www.sibername.com (a bit pricey but at least they allow PayPal, which is good in a pinch.)
There are a whole bunch of others that would do you just fine. You just need to do a little more homework, that's all.