Grain of salt "I spent 7 years in the game, but haven't played in 2+ years": The short answer is it will degenerate down to 60 permanently, but not for the reason you may think.
Post-60, you have an invisible shared pool of 40 points to allocate to raise the rest of your craft levels past 60.
Switching to Woodworking from Cooking won't decrease your cooking levels at all. What actually decreases them is leveling Woodworking past 60. As you level Woodworking, your Cooking levels will decrease to compensate so that way you don't exceed the 40-point "limit". So when you hit 70 Woodworking in your scenario, your Cooking will still be at 90.
If you have multiple skills 60+ I have no insight on how the mechanics on that works, but most people don't do that.
Bonus Info: A lot of old-school crafters used to use this fact to break multiple crafting success tiers on multi-craft items like the Haubergeon in order to increase the HQ rate (I'm going completely from memory, but I think the magic number for Smithing was 91/92, since the Smithing cap is 61. The rest of the points went into Leather or something to hit the 10+ success tier).
Most people, Beastmasters in particular, usually (used to?) make a mule just for cooking. It's more expensive/time consuming that way to "max out", but the cost of skilling 60-100 (or even 90-100 alone) is usually not recoverable by most people for any craft that isn't based on consumables like Alchemy.