BROKEN RIGHT ARM!

for more ideas, see this thread from approx 2012...larger question than yours...all cooking (rather than just pasta) when a member had surgery and only one hand available to cook
https://food52.com/hotline/13262-if-you-could-only-use-1-hand-your-dominant-one-while-cooking-what-would-you-make-assume-you-can-u

This is in the same vein as most of the comments here, but this recipe from serious eats is pretty great too! http://www.seriouseats.com/recipes/2014/10/pasta-pancetta-shiitake-mushrooms-parmesan-recipe.html

You can cook pasta in a skillet with,generally, much less water; or an asparagus pot works well, you can just lift out the insert. Or make long noodles (although that might be a bit difficult with one arm) and lift them out with tongs.

So sorry about your arm! Lidia Bastianich would say to use a spider, a long handled tool that has a lot of holes or is made of an open wire. Just scoop out the pasta from the hot water.
I'd say to try using a cooking pot that is wider rather than high to hold the water. Put the pan on the stove, empty. Use a pitcher that you put under the faucet, fill with water, and pour that (with your good arm and hand) into the pot.
Let the water completely cool off before you dump out the pot, just ignore that pot of hot water on the stove for an hour or so. Bail it out with a bowl, small saucepan, whatever.

And hope you feel better soon!

For pasta, Martha Stewart's one-pan pasta (a "genius" recipe on this site). It's pretty flexible -- many possible variations -- and works well.

Could you use a colander or strainer to lift the pasta out of the water? Then leave the pot on the stove until the water cools. Or use farro in place of the pasta. It's just as good and cooks in much kess water--and a smaller pot. Best wishes for a speedy recovery. When I was out of commission a few years ago, a doctor-friend reminded me that beer and wine had superlative medicinal properties.

Probably.
Saying yes from analogy.
There are some lasagna noodles designed for baking w/o boiling. But, truth to tell and purists look away now, all noodles can be cooked without draining...just need enough liquid.
Sauce may be added from tHe start, or after the noodles are cooked.
Those with slow cookers who have done this will be able to provide settings or more detailed instructions.
Wishing you full recovery on the armm