There a couple of things to consider. The employer recognition is the main thing. If the employer isn’t willing to engage with the proposed union, would it actually serve your interests to switch?
Even if it does, can you still have subs deducted from your salary or would you have to pay yourself?
If after these considerations you still want to join, contact the proposed union to ask about membership. As has been said, they may be reluctant to be seen to poach members. On the other hand, if you’re willing to leave the current union, this may be less of an issue.