There is the option for removing trivial skill checks, as mentioned elsewhere in the comments of this post, but most players I've had want to roll for the small stuff. Just expecting you succeed gets really boring after a while. Not to mention a lot of us bought shitloads of these clicky math rocks and want to use 'em. So while that's an option it's not one that I'm a particular fan of. Advantage I'm also not a huge fan of as it then feels like it cheapens advantage itself. I use both advantage and disadvantage sparingly in my games and have outright banned Silvery Barbs at my table for that reason. When you get advantage or disadvantage from something I like it to feel like an "Oh fuck" moment. A friend helping you out in a time of need or an something catching you completely off guard. My idea would be confirming critical failures.

For combat I understand a simple natural 1 equals a failure. That is under pressure and yes you can choke in those moments or just be bested by an opponent. But for skill checks you're proficient or an expert in during a non-pressure environment or situation it makes no fucking sense. Cut that chance down by making them confirm it.

Natural 1 on a Proficient Skill = Re-roll the d20. If you roll 10 or below then you critically fail. 11 or above and your result is treated as a simple 1 instead of a critical failure.

Natural 1 on an Expertise Skill = Same as above but the failure bracket shifts down to be 1-5 for a critical failure and a 6-20 for a simple 1.

That's how I'd run it anyway. Maybe shift the failure/success brackets but the same basic set up.