My birds LOVE dried peppers, the Higgins California Blend and the Tropimix seed-mixes contain dried peppers, cayenne I believe, and Kane goes absolutely insane for them, he rips them open like they are full of crack or something and eats the seeds like he's not eaten in weeks! They also all love fresh Bell Peppers, though I've not tried any other fresh varieties...
The Wegmans her actually sells packages of different types of already-dried peppers, they have a ton of varieties, everything up to dried Ghost Peppers...And they're cheap too. So I often buy a packaged of dried Chillis or Serranos and use them to bribe Kane with, works like a charm...
I absolutely would not try to dry peppers in your oven, microwave, dehydrator, etc.! That's going to end very badly and you're going to be extremely sorry that you did it, because you're not actually "drying" them in the oven at all, you're "baking" or "roasting" them, and that will only result in all of the oil being released into the air...Now the first problem with this is that all of the flavor of the pepper that your birds like will be gone, where as if you actually hang them up and dry them, the oil doesn't dissipate into the air, it remains in the peppers...But that's not the real issue with baking them/roasting them, because the second that oil hits the air in your house, you're going to go from everything is fine to agony in a few seconds flat! And if you're using any really hot varieties then forget about it, your lungs will burn and you'll have the worst coughing fit of your life, and at the same time your eyes are going to be burning and watering for hours....I don't know what that would do to your birds, but I'm assuming the same thing...They can eat hot peppers because they don't have the taste-bud receptors for capsaicin, but that has nothing to do with their lungs breathing in the oil, so my guess is that you may even end-up really hurting them or worse if you do that...
If you have a dehumidifier, then stringing the peppers up in a closet or small room with the dehumidifier running would work...Like a pantry would be perfect...