You could say you're fixing it or it's the "phone graveyard"
If you have other dead/useless phones, mix them together and I doubt she'll check them all.

Remove the battery/sim and store that somewhere you keep small electronics/batteries.

... my hobby phone because it's with me everywhere I go.

My phone is double password protected, so if anyone finds my phone, they need to know the 2 passcodes just to get to the main screen. If the phone is ever lost or stolen, I can track it down by GPS and manually shut off the phone. The phone then becomes bricked.

Just about everyone that I know have their own cell phones, no need for them to use mine.

Serpius

But seriously,

Best to never have it in the house.

Keep it at the office, or maybe in a LOCKED glove compartment of the car.

Never leave it in your clothes.  All wives go through pockets all the time.

a friend of mine once told me he hid his in an old golf bag.  There are all kinds of places to hide it, but it seems to me, away from home is the best idea, somewhere your SO does not have access to.

Swim

If you have a concealed carry permit

Buy a gun safe for your car and keep it in there.  I have kind of a cheap one, but you can get them with fingerprint recognition.

That's before I started to use Google Voice. I now use Google Voice when I hobby and delete it when I am not.

If you don't share a car with you SO, then the spare tire compartment I have heard is what some gent's do.

Having a hobby phone AT ALL is a risky proposition. Most people keep their phones for a while (years?) - the discovery of a strange phone will not be easily explained.

No matter how out-of-the-way you think your phone is stored, that won't stop a wife from one day saying "I'm going to throw out that old golf bag/clean out that unused drawer/etc" And of course she will look through it before throwing out the bag or cleaning the "hidden" drawer.

Hiding in a car is even worse, as you may think you never swap cars, but one day your wife's will be in the shop and she will quickly borrow your car, without asking. Or maybe she does ask, and now you're left stuttering and sputtering...

How about not having a hobby phone? Unless you wife goes through the phone bill with a fine-toothed comb, but in this day of unlimited minutes, who does that? Or learn how to use Google Voice from your phone, so those calls don't show up on your bill. Same for texting - there are tools out their that use your data plan for texts, so they don't show up on your bill.