Yes, it is easier than it looks actually
Just use {if} statements around the columns in home.tpl.
To show the right hand column on all pages except the product page and cart pages, use this around the right hand column:
{if $main ne "product" and $main ne "cart" and $smarty.get.mode ne "checkout"}
For the left hand column, use this to show it everywhere but in the cart & checkout:
{if $main ne "cart" and $smarty.get.mode ne "checkout"}
See if that does the trick for you