Got a ZZr600 myself, what you describe is normal, leave the bike to warm up on the centre stand in neutral till the rear wheel stops turning, which is good practice anyway allows the oil to circulate.
Mine takes about 3 or 4 minutes, It’s caused by the viscosity of the cold oil causing the clutch plates to drag – also the kawi gearboxes are notoriously clunky especially 1st to 2nd.
If you haven’t already done so check out zzrinternational forum it’s a gold mine of information on these bikes including it’s bigger brother
How’s you idle speed – should be @ 1100rpm