Unfortunately you will always pay paypal fees per transaction (not much - up to 3.4% + £0.20 GBP per transaction).
In 'paypal' case shopping cart is only a part of your website design (what customers can see) but all transactions are still processed by paypal on their secure servers.
Then you've got few options:
1.You can use their free solution which is working fine but doesn't look too good, as every time customer will click 'add to cart' or 'view cart' button, will be re-directed to paypal site (kind of virtual cart created in real time for current transaction purposes). Like I said, it will work fine and many shops using it as it's easy and free.
2.You can use paypal shopping cart which looks good and everything is 'happening' on your website directly but you will have to pay monthly fee (regardless your transactions).
3. You can use paypal together with shopping cart developed by third party. It can be free or paid. On my website I'm using free cart from
www.fatfreecart.com .This is an option somewhere between 1 and 2 and as long as customer adding more products ect., he will see this nice 'fat free' popping up cart. But once decided to pay, will be redirected to paypal website to finish transaction.
Hope you know what i mean

I'm not saying that my solution is the best couse it's not. The best is to pay and get professional and good secured cart from paypal (or other). But as for now I'm not making money on my website, this is the best for me, looks smart and it's easy to use (if you know basics of html, to copy a piece of code in right place)
If you would decide to use option 1 or fatfree cart, I can explain how