There is lots of good advice already offered here by Dalvers63 and 8b8ll. There is one more piece I would like to add.
Most carpets are nippy as babies and outgrow this. Baby or not, most are always aggressive in their cage (carpet or any other snake). You need to find a way that works for you on getting the carpet out of the cage.
Your best bet is to use a hook but I see that you do not like hooks. The next logical thing is to use a rolled up newspaper or empty paper towel roll. When you open the cage, rub this object across the top of the snakes head, most times this kills the feeding response. You then can reach in and pick up the snake. It will take a few times for this to work and the snake to associate the rubbing on the head as a handling or cage cleaning time. Once the snake gets accustomed to this, you will have a much more pleasurable handling experience.