If you participate in an illegal strike your union will lose all credibility with the management and they will have NO chance of negotiating a decent deal.
One of the bargaining chips you have is that the company are desperate to avoid the negative publicity of industrial action and you will throw that away by doing this.
Let the union try and do the job you pay them for, don't screw them & your colleagues like Tea or Coffee over by striking against their advice.
I really want you guys to get the deal you deserve but idiocy like this makes me wonder what some of you are thinking.