You should be able to get a new pick for around $10. I would not trust reusing one especialy when a new one is so cheap. If you do reuse it be sure to weld it on.
The old one has allready been compressed/pressed and will not be as tight in another pump.
The way I have installed in the past is to find a wrench that fits over the tube but will not slide past the flange. Make sure its lined up then tap it in with a hammer on the wrench as close to the tube as you can. I think there are special tools for the job also.
How have others done it?