Removing OEM air intake w/anti-shudder valve

Is there a 3rd party alternative that filters the air, even if it doesn't cut the intake on shutdown? If so, is there any risk of the engine not shutting off?

Not sure as to the context of what you are asking, but the OEM Mann air filter is very good at what it needs to do. No need to modify something that works perfectly fine, even for mildly modded engines.

Normally it does work fine, 15 years in my case, until it stuck after a cold start when I didn't drive very far. So I'd rather replace with a filter than reduces airflow on shutdown, rather than cutting it off entirely. It seems like VW added an anti-shudder valve more for aesthetic reasons, if there's no risk of the engine dieseling on & on after turning the ignition off.

I sense your terms are confused. The ASV and the "air filter" are different animals. Completely.
If your ASV is sticking, or misbehaving, try cleaning it (off the car) or replace it. 15 years and some stuff is going to go.
And yes, the ASV can prevent runaway (and the attendant death of your motor). There's nothing aesthetic about it. Other than it's small and kinda cute.

Yeah, fix your problem, don't try and reinvent something. You said yourself it worked fine for 15 years... probably just needs to be cleaned. Not a big deal. Don't overthink it.