Hi there,
Do you have a polytunnel, greenhouse or cold frame?
The reason I ask is that I just use my propagator to sprout my seeds. Once they have their first two leaves & the majority look good & strong I take them out and leave them in my polytunnel covered in fleece.
First though I would leave them at least 24 hours without the lid on or with it opened, my propogator at this point in the season is in the polytunnel.
When I take them out I make sure that they are either on polystyrene, black plastic or warmed soil.
Plants need to be gradually hardened off, otherwise they do not grow well & can become weak & spindly.
The only seedlings I leave in for any longer than this are my tomatoes, peppers & curcubits.