Any other suggestions than a burner phone, I am worried that it will be discovered by the wife.
 
I have a type of calling card (via Reliance Global), but you can only make international calls with that. Are there other calling cards you can use locally (US). Problem there is they can't call you back.
 
THen I looked at google voice for my smart phone, but not sure how that would work?  Can I initiate calls with that so it doesn't show up on my phone bill? Any ideas

Consider running your google line or whatever contact number you obtain though google itself BEFORE you begin contact.  Make sure the number is not already attached something to much more ridiculous than what you would like to represent.  
I have had royalty from the south pacific and the wife of a wall street broker, contact me just today.  

I have a Skype account, but I don't have a number through them.  Not sure if that would work.  You can delete the call history, I believe.  It does ring on all of the devices that you have the account set up with.  Not an issue if you just have it on your one phone though.

Great app. Gives you a number. Nothing ever goes on phone bills. Works crystal clear thru wifi but also ok through cell towers. Just link it to your email.

I have a cheap 2nd phone bought for like $10 that I keep in a drawer and pretend its an old phone that I never sold or gotten rid off. I use AT&T prepaid for it its like 10c a min per call with 20c texting, use it maybe once a month and when I don't use it I take the simcard out

Can you get incoming calls or texts?

I checked this out, looks good

app for iphones? Or just a disposable mobile phone?  

I have a local Skype number and forward it to a international phone and works good

I suggest you use an outside BBQ to burn your phone but really just using it for a wheel chock on a truck is pretty much as effective.  (Just Joking)  Trak Fone.  My Grandmother keeps a burner phone in her car.  Doesn't use it...  just there for emergencies.