The Talmud explains that God Himself 'changed the truth' – by telling Avraham that Sarah said that she (not Avraham) was old – in order to maintain
shalom bayit, peace between husband and wife (Baba Metzia 87a, Rashi on Genesis 18:13). By going to the mikveh, you are maintaining and nurturing the relationship with your husband, and there is no greater
shalom bayit. Making up an untruthful excuse is okay in this situation.
You may want to immerse at a mikveh closer to the wedding hall so that you can get to the wedding sooner. You could also explore the option of going
after the wedding by making special arrangements to g
after usual hours. This can be worked out in many mikvaot, sometimes for an additional fee.