At a guess, i would do it as follows..
Aircraft arrives on chocks.
No 2 Engine Shutdown
A/C Steps to the R1 door
Refuel Connected & Started
No 2 Engine Oil levels checked etc / RH side of a/c walkround carried out.
Refuel completed & Disconnected
Crew member on board, R1 a/c steps removed, No 2 engine started.
No 1 Engine Shutdown
A/C Steps to L1 door
No 1 Engine Oil levels checked
LH side of a/c walkaround carried out
Crew member onboard, L1 a/c steps out. No 1 engine started.
Taxi out.
The key here would be that the minimum amount of people around the aircraft, with fire cover in attendance