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The problem is, you need much more info about users to set up an account for ecommerce than a CMS would ever require. Combining the two under one registration seems like a good idea, but asking for real names and full address details would dissuade many people from registering on your site if they don't particularly want to use the shop feature.
I would redirect users to a standalone ecommerce app that is right up to date and has a track record of reliability with order processing and payment gateways.
Ecommerce software need to be bullet proof and as site operator, you can bring a lot of trouble down on your head if you use a buggy app that messes up transactions.
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