We all know how vague Irish legislation is towards traps and trapping! So I don't think the op has broken any laws here imo!
The fact that he's using live cage traps, in a area with lots of birds present, shows he's taking into account the risk of non targets being caught.
Now, I for one have never caught a pheasant in a squirrel cage, so recon it don't happen very often. Sometimes a non target gets caught no matter what precautions are taken. Shit happens!
On another note, I do believe the op thought that bird was perfectly fine to release, or he would have dispatched it! Seen it