Easy way to catch them, use Endeavor. have a high level Pokemon, with 1 HP remaining. They should be faster than Regi's, use Endeavor, then most likely the Regi will KO you. Switch to something with a Sleep (and Sleep effect only attack) or Paralysis and throw the Ultra Balls, and whatever other balls you want to use.
Endeavor, assuming you have only 1 HP, will assure that whatever you attack will have only 1 HP. It subtracts the difference of HP between attacker and defender. So if Regice has 300 HP, you have only 1, then the attack will do 299 damage, untainted by any stat increase, or decrease, defense ect.