What is the best way to replace my VB's EXE, in each of the user's pc's ?

I am working on a pgm that will be used on a local LAN (approx 10 users).
It is VB6, and it uses an Access DB (97). (DB will be on the server.)
It is being tested by users, and there will be frequent updates to the source code.
Each user has a copy of the pgm in a folder in their 'C' drive.
I have already solved the issue of the pgm knowing where the DB is located.
The end result of that solution being, each user has the required path stored in a local INI file.
At the moment there is only 2 users testing it, and only one of them has Winzip.
Emailing the latest version to him (him with Winzip), is pretty easy, and guiding him to replace his EXE, is also easy.
The second user does not have Winzip, and the Windows XP zip extractor is a pain in the butt.
(Hard to find where it went, and it's creating parent folders/paths instead of just extracting the EXE.)
I tried sending the EXE but it got blocked.
If I tried creating a winzip self extractor, I presume it too would be blocked.
Here is my proposed solution -
I will have a version of the EXE on the server.
Generally it is not used, but it will be, on rare occasions.
When I compile a new version of my EXE, I will somehow earmark it with a date/time or a version number.
I will send it to the user with Winzip (the owner of the business).
He will unzip and replace his EXE.
When pgm starts, on any pc, it checks it's 'version' against the copy of the EXE on the server.
If the server's version is older, it will offer to replace the version on the server.
If the server's version is newer, it will offer to replace itself with the version from the server.

Does all of that sound feasible ?
Can the EXE replace itself, whilst it is running ?
Is there a better way ?
Any words of advice prior to me starting on it ?

Thanks,