Separation is separation - if you can achieve one of the separation standards then you have done your job. In good weather (here in the UK anyway) we can used 'Reduced separation in the vicinity of the aerodrome' where, if the controller can see both aircraft and can assure separation between them, you have achieved separation. There are a couple of other procedures that can be used too but for a G/A I'll keep an eye on them myself. I'm pretty sure the UK rules are based on ICAO SARPs. This only works for the initial period immediately after a G/A of course, but it's usually enough to time to set up radar separation or something else.
If the track of the G/A and the departure cross and the aircraft are in copnflict then it will be necessary to modify the route of one or both aircraft. Some units have standing procedures that say what the aerodrome controller can do whilst at others the aerodrome controller and approach controller will have to co-ordinate a suitable solution.
In poor weather when the aerodrome controller won't be able to do visual separation and the aircraft will get close if there is a G/A you might want to pre-agree a non-standard G/A with the approach radar controller. In LVOs we have to have bigger spacing between inbounds and departures have to be airborne before an inbound reaches 4 miles, in part, to prevent conflicts between inbounds and G/As.
Hope this makes sense.