JetBlue serves no peanuts, and I believe they'll refrain from serving nuts on your flight if you ask them ahead of time. Of all the airlines I've flown, they've been the hands-down most consistent, and had the absolute best and most accessible customer service.

Cashews aren't an issue as far as I know. But that's not something I want to try, you know?

I have no idea if they service your area, but Jet Blue rocks. 

Later this spring we are taking Allegiant Air to Arizona.  I've been told -- no peanuts. 
I've never flown this airline before -- American and United are our usuals.  My kids seem not to be inhalant-reactive, however, so far.

From what I've experienced - American, United, US Airways (my standard 3 pn free airlines) all have warmed tree nuts in first class (I usually don't smell it if I sit on the wing or farther back) and all have a buy-on-board option which includes a pack of tree nuts.

I think calling each and asking for the disability coordinator specifically and find out which can give you a buffer zone will be the strategy. Then, of course, talk to the flight attendants on the day to make 500% sure they won't walk through the coach cabin with warmed tree nuts as their own snack in the back of the plane. That happened once, and 30 minutes after I went back, made them get the head flight attendant, and chewed them out nicely. Just so happened they weren't supposed to do that anyway and broke the rules.

Good luck!  Other options to consider, not sure how far you are from where you are going in AZ -- is train or driving?

Adrienne