Providing your current cart has an export function to CSV there’s a possibility you can save some time re-importing your products
It’s possible, but it’s pretty likely it will be complicated and time consuming.
I assume your existing cart is not CS-Cart. It is unlikely you’ll be able do a database export and import directly into CS-Cart. Both carts would have to have identically structured db’s, which they won’t, just won’t happen.
If you want to try to move your product info via import, then confirm if your current cart allows you to export product info into a .csv file. CS-Cart has the ability to import product info from a .csv file and you can export from CS-Cart to get the format you need for importing. Compare the .csv files from the two carts and identify what variable names used in your existing exported db .csv file are equivilents to the variables used in CS-Cart. Basically you have to rework your exported .csv file to exactly match the CS-Cart file, which is no small feat, but if you have a lot of products and product info it may be worth doing.