I think, what you're trying to do, is to use Zimbra as a webmail as a main purpose. It's not designed for this, or, even, if you can achieve the result, it would be big overkill for your needs, or introduce unnecessary burden to troubleshoot mail traveling. If you still consider some "vague solutions", here are a couple of ways:
1. Register your users on your ZCS server, and create external accounts for each of them. Provide relevant POP/IMAP data and hostname. By this, Zimbra server will go to your hosted mail server on intervals configured (I think, default was 1x 5mins), and fetch mails from hosted mail server. IMAP connection in this case would require the same amount of storage for account on hosted Mail server as on ZCS server, but that would be the most reliable. Or, if there are any problems with mail reception, they could be troubleshooted at Hosted mail server side.
2. Configure a single account on Zimbra server, and set it to be CatchAll account:
As a Zimbra user, run this command, substituting your domain:
Additional info from here (not particularly for your situation, but any way, more info is better): Ajcody-Migration-Notes - Zimbra :: Wiki
$ zmprov md YYY.state.XX.us zimbraMailCatchAllAddress @YYY.state.XX.us
When you start to receive all mail coming from hosted mail server in this account, add Incoming filters, by catching To or Cc field content, and forwarding messages to internal user accounts. Note, that there would be no way to catch Bcc field content, or re-route e-mails, that are sent to mailing lists with a single mail address, as you can not write a filter for this.
But in this scenario, you still get too much complexity and ways to fail in mail communications, and it does not relieve you from burden to setup zimbra, dns and outgoing mail issues anyway.
In essence, I do not think, that it's viable to build any of these, if only you do have any specific particular needs, that such overkill is worth it. Just put all on ZCS server and you'll be in control.