I am currently using v.1.5.1
They will not have to do both, nor will I be transferring new customers from one to another, just existing customers that already shop with me
Make sure to create your new cart with this same version fresh

Then you have options
1) import only the customer related tables
address_book
customers
customers_info

Enter the products you want manually

2)import the full database and delete from the admin the products you do not want
There may be some issues with orders etc and my account display owing to deleted items