You can try to connect the OPN to your iPhone DIRECTLY via MFI and not via the Connect Clip to the iPhone while you’re using the Connect Clip for your PC. Then It’s no longer an issue of whether the Connect Clip being able to be connected to 2 devices at the same time or not. It’s now an issue of whether the OPN can be connected to both the Connect Clip AND the iPhone at the same time or not?
While I don’t have the Connect Clip and I only have the TV Adapter 3.0, I surmise that the answer is yes. Case in point, I have the TV Adapter 3.0 connected to my laptop and I watch YouTube videos on it. While I’m watching (and listening on the OPN to) YouTube videos, my OPN is also connected to my iPhone directly via MFI. While I can’t simulate am incoming call to test out your situation, I can just play a song on my iPhone’s iTunes app and I can now hear the song from my iPhone, while the sound from my YouTube video from the laptop (coming from the TV Adapter 3.0) automatically gets muted. Now if I stop playing the iTunes song from my iPhone, in a few seconds, the YouTube video sound from my laptop automatically resumes on my OPN.
What this tells me is that the iPhone MFI connecting to my OPN takes priority over the TV Adapter 3.0 connection to my OPN. But all the while, the OPN has established connections to both devices, and the OPN MFI connection to the iPhone seems to have priority over the OPN connection to the TV Adapter 3.0.
Now if you replace the TV Adapter 3.0 with the Connect Clip in your case, assuming that the transmission protocol used by the Connect Clip is the same as that used by the TV Adapter 3.0, which I think is most likely the same, things should behave the same way as I have experienced with the situation as explained above, and you’ll be able to take your iPhone incoming call while you’re having your Skype call. I just don’t know if the Connect Clip mic will automatically mute for you or not, but even if you have to manually mute either the Connect Clip mic or use the Skype keyboard shortcut for muting, it’s worth a tap on a key to mute the original call in order to take your iPhone call.
You still should be able to use the Connect Clip with your iPhone calls for hands free operation using the Connect Clip mic of you want while you’re not on a Skype call, by connecting the Connect Clip to your iPhone normally. But when you’re on a Skype call, the Connect Clip will be connected to your PC and no longer to the iPhone, in which case the OPN MFI connection to the iPhone should automatically take over as long as Bluetooth is still enabled on your iPhone.