One who bli neder has the minhag of being Mekabel (accepting) Shabbos 20 or 30 minutes before Shekia (sunset), and now that time arrived and he has not yet immersed for the honor of Shabbos, is it better to be Mekabel Shabbos immediately or to go immerse even though he will be handling money after the time he is normally Mekabel Shabbos?

Assuming that the Mikva is at the same place he is davening Kabbolas Shabbos, he likely has anyway the money with him and has to put it away. He may just leave some by the Mikva. Also assuming that he has already davened Mincha, and his minhag is also to carefully do Tevila on Shabbos, he could be Mekabel Shabbos, then immerse following all the Shabbos needs and proceed to attend Kabbolas Shabbos in shul.