Pavouk106:
To be sure, once more - Can I connect 6.5V supply to 5.5V (not fully charged) capacitor without damaging it if I disconnect the supply before capacitor reaches its maximum voltage? If I can do this, there is absolutely no need to use any kind of regulator
Yes if you have sufficient series resistance between the 6.5V supply and the capacitor. "Sufficient" here means much higher than the internal resistance of the capacitor (the ESR measured at DC).