Arc welder ? What kind of arc welder ? MIG, MMA, TIG, ...?
It seems to be MMA, but I am not sure.
The principle of working you choosed seems not to be right.
The welder must stay on all the time, but, when you detect a current, you must turn it off after an adjustable delay.
So, there is no problem of turn on as you can use a soft start circuit.