Electrical Discharge Damage
How much of a discharge will it take to kill a person? Well after a quick google search the minimum fatal amp value seems to be around 20-70 milliamps of current across the heart. so so long as the discharge is lower than that then they should survive,
You've said the power is not strong enough to kill, so one would assume that that would mean no matter where the arrow hits it is designed not to kill so would need to be lower than the upper estimate of 70 milliamps. however you have designed a magic that won't kill and then added it to a weapon that IS designed to kill... an arrow...
Would the freezing arrow make it much worse? no actually. Ice is actually a fairly poor conductor, and it is actually the ions trapped within the ice that allows for the electricity to be conducted. so if the magic imparted the cold damage before the electric damage, then actually your making the electric damage less powerful.
If it was just Flash freezing the surface of the body, then it'll be painful but no long lasting effects. however if the freezing had depth and enough strength then it'll cause frostbite (at the lowest level) which can easily be fatal especially if its deep into the shoulder, and if not fatal then it will probably render the arm and should next to useless for the rest of the victims life.
If your arrow has mass roughly similar to a regular arrow then being launched at "javelin" speeds could still easily kill a person. if it hits the shoulder then it could still break ribs, the shoulder blade, to severe damage to muscles. if it is an entirely magic arrow and has no mass, then all of the above doesn't really matter. Its magic, the spell that causes it is designed to either kill or not kill, and its up to you as the writer what effects it causes
Non Fatal Magic
If you want to incapacitate a person with magic without causing last damage, then get rid of the freezing aspect (Personal Opinion) stick to emulating what happens in real life. Tazers use non fatal amounts of power but over a continual discharged it incapacitates the body, (and apparently is extremely painful) but unless a very rare set of circumstances come together it is non lethal.