Up to the policy of the bank in question, it can be done but some banks insist on taking out a new mortgage in joint names and clearing old one in which case you would lose tracker rate.
From the point of view of what if something happened to you, you can take out life cover to clear mortgage in event of your death without being named on mortgage, you could also take out serious illness cover, income protection again if you wanted to, as far as i know only thing you could not do is mortgage repayment protection which is the one that would cover you if made redundant however this has gotten expensive, claims are difficult and depending on your employment might not be that easy got anyway.
So it is not worth losing the tracker rate if the bank insist on a remortgage, leave things as they are and just make sure you have enough life cover for the mortgage and any other cover you feel you need and can afford.