Richard Landrine, please provide contact info, and what is the prior platform, and current format(json,csv,shopify-csv) of the order data?
If you've already had success with cart2cart, contact them about your concerns, as they provide that service addon for $49. Despite the cost just having the support for all the edge cases is worth it. This should only be an issue if the previous import did not preserve "ID's" and somehow new orders will conflict with what now exists in shopify's admin.
There is also https://apps.shopify.com/orderimp which can also populate customers...
A thing to know is most ecommerce "order ids" are basically titles|numbers(customer order#) and not system-locked-ID's, they are for human convenience.
Alternatively reach out to me by email in my signature, if you still need this or a custom app should this become a recurring issue.