If you remove the ability to take something out of the cart, then the only way to get rid of a selection would be to abandon the cart and start over. With online shopping, abandoning the cart means leaving the site for over an hour. Eventually the customer would become frustrated, and go somewhere else.
To remove that column, go to the managecart function in nopcart.js and find the column heading:
and remove the blue portion.
Now remove this line in the cart body:
strOutput += "<td><input type=button value=\" "+strRButton+" \" onClick=\"RemoveFromCart("+i+")\"></td></tr>";
Finally, you may have to adjust the columns at the bottom of the cart, starting with the subtotal and working down.