The upload seems to occur immediately after the video stops recording, so it helps if you've got Wifi. I also noticed that if you delete the video from Qik, it is also deleted from your online storage (with no apparent recovery method?). If you're forced to delete the video under duress, there would be no online copy for you later.
Potential solutions I can think of (haven't tried any of these, please test first!):
1) Share videos as public by default, and enable the Qik option to publish to YouTube immediately.
2) Once under duress, turn on (ironically) airplane mode on your phone, ideally surreptitiously. Then, when forced to delete your videos, you can do so locally without deleting Qik's online copy.
3) Set a password on your phone and refuse to unlock it for anyone. If they insist, you/they can input a wrong code several times and cause the phone to wipe itself. Your video will still be preserved online.