Do you have a heating pad you can use?
I've raised my chicks with a
Mama Heating Pad and they're usually fully feathered by 4-5 weeks old. But chicks raised with a heat lamp don't have the opportunity to be exposed to cooler air regularly and their feathering and acclimation is usually delayed. The benefit to using a heating pad cave is the chick will choose how much heat it needs and you won't have to worry about regulating an exact temperature.
At 2.5 wks, your silkie will probably still need some heat for a couple few/ more weeks. If you can set up a MHP in maybe a dog-crate brooder, or something that will keep your older birds safely separated, your chick can go right out to the coop and you can start
See But Don’t Touch and hopefully achieve an easy integration in a few weeks or less. Here's another link for adding chicks to your flock:
Integrating at 4 weeks old
If you can't get electricity out to your coop, you can finish raising it in your house, but I don't think an ambient temp of 22C is warm enough, your chick might end up complaining quite a bit, especially if it's used to a heat lamp. And the integration will take so much longer.
Probably the only way your Silkie hen would raise a chick she didn't hatch herself is if she's currently broody and has been actively sitting on a nest for at least 2-3 weeks, and even then she would likely only consider adopting day-olds.