[Closed] WHM/cPanel help - Web development without access to domain

One for the developers, I'm not expecting a flurry of replies but any light shed on this would be greatly appreciated. I've a new Linux server and trying to get my head around what is possible are with it.

This is generally my process:
- Set up cPanel account for new client/website
- Build site hidden from search engines but accessible on a sub-domain (dev.client-name.co.uk)
- On completion move site from sub-domain to main (removing & redirecting old site if there is one) and allow indexing on www.client-name.co.uk

To me this is as simple as possible and means minimal fuss on migration as website files and associated databases all stay put and is done with just a few changes to DNS etc.

I'm trying to find a work around for when a client has an existing site with no access to it or DNS - we would get this access in the end but this would save some faffing about. Ideally I'd like something like:

- Set up cPanel account for new client/website (www.client-name.co.uk)
- Build site as usual using their cPanel account but make site viewable on a sub-domain of my website (client-name.mywebsite.co.uk) and also give me access to Wordpress etc through that subdomain.

I can't get my head around if this could be doing using redirects or aliases, or indeed is even possible and I should stick to physically moving files/db etc from a staging area to a live site on completion.

Any thoughts much appreciated!