I currently own several domains on which I am using a Whois privacy protection service to hide my personal details. In the near future, I would like to transfer some of these domains to a different registrar.

It has been many years since I last performed domain transfers, so I am no longer knowledgeable about what it involves. However, I have read from several registrars that they ask their customers to disable Whois protection before effecting a domain transfer. Since there are several websites out there that publish archived versions of Whois information (and ask handsome money for the information to be hidden, of course), I would prefer to avoid having such a "gap" in my privacy protection.

I figured that these websites would fetch Whois information mainly when a query is effected through their own website. However, I have found out that at least one of these sites had a copy of the Whois information for a new domain up on their site within hours after I registered it, so they must have some other source (of course I used a Google search to find that out, not their own site). What that tells me is that the time it takes for the domain transfers to go through would be more than enough for these rogue websites to cache my information.

If my new registrar offers privacy protection for domains right from the point of registration as well, is there no way to transfer the domain between the two without reverting to my default Whois information in between?