Are you upgrading again from Series 4 cellular to Series 5 cellular?
If you're keeping your Series 4 cellular and just upgrading the phone, you'll be fine. You get a couple of options when unpairing the watch - you just need to select "Keep Data Plan", and it'll remember the plan when you pair with your new phone.
The problem, as you say, is when you're upgrading from one cellular Apple Watch to another, whether via warranty exchange or upgrade from one Series to another and require EE's intervention.