My company is getting a new business system which is phasing out my position. Another position may be offered to me but it is on a different shift than what I am on now and the position is not only a desk job but physical. What options do I have if the job is not for me or the shift?

If they are changing the fundamental terms of your contract without your approval, this is by definition a constructive dismissal and allows you "resign" and treat the "resignation" as a termination entitling you to a severance package. Please note that the law is significantly different between Ontario and Quebec so if you work and live in Quebec you should consult a lawyer in your province.