How can we lower the risk of migrating from an old site to a new site?

background knowledge about our app so you can have context :

we are a multi-vendor B2B e-commerce website
our users base is fairly small, with about 400+ active customers
most of our users are middle-aged men and don't have much experience in using tech
We have an old e-commerce site that was built using an old e-commerce platform, it served us well but we grew out of it and built our own custom e-commerce platform

these are the main risks we are worried about :

the new site's UX matches the old site by 60%-70% so because of our demographic we are very worried that not negligible part of users might get discouraged using the website and because we are a B2B site even a small percentage of users can equal a lot of orders/money.
when we launch the new site we don't want to kill the old site right away, we want to keep it running as a backup plan till we know for sure that the new site is stable, but that will raise a few concerns :
should we let users use the old site and place orders?
should we synchronize between the old DB and the new DB (it's tough technically) so we can have a single source of truth?

thanks a lot :D