First, a 2 KW generator is a small generator.
Given a choice in how to do it when a blackout happens I would start the generator but totally reduce the load as low as possible before switching over to the generator. I only suggest this because the generator is so small.
I have an 18 KW whole house generator with fully automatic transfer. When power fails within about 7 to 10 seconds the generator is online and has no problem doing the transfer under the full load the house is providing. This is typically about a 4 KW load since I have not yet transfered the air conditioning over to the generator yet. However, given a choice in the system you describe I would eliminate as much load as possible and then bring the load up slowly. Since it is a manual operation that should be easy enough to do.
Just My Take
Ron