There are many different types of mouse traps. (Example old fashioned snappers, new electrocution, confinement, sticky) my question is would some on these be assur because of tzar balei Chaim ( the prohibition of hurting animals)? Such as the sticky traps, the mouse starves to death. Do you have to ensure an immediate death I using one of the killer traps or can you use a more convenient or cost efficient model?
Tzaar Baalei Chayim is permitted for human benefit, even monetary loss. The Gemara in Shabbos allows leaving heavy bags on an animal when the alternative is to cut the rope, allowing the packages to fall and break.
We also find in Avoda Zara how they used to de-hoof an animal when a king died, in some form of honor.
How to weigh the significance of the loss against the pain, I don't know.
As partially noted by HaLeiVi above, there are many reasons why Tzaar Baalei Chaim is not a factor here.
These Teshuvos (1, 2) both note that the concept of Tzaar Baalei Chaim does not apply to mice, as it only applies to animals that do work for humans. They bring various sources for this, but also note that many Poskim disagree. It is their opinion that even those Poskim hold that in such a case it is allowed to harm an animal that is annoying or harmful to humans, perhaps because of the below reason.
It also seems to be an accepted Halachic opinion that for human benefit, Tzaar Baalei Chaim is allowed. See for example, Rav Eliezer Melamed here. He also quotes an important source to this discussion Igros Moshe Ch"M 2:47, who says that ideally, one should avoid killing them directly with their own hands, so as not be become רגיל באכזריות. See Rav Melamed's article above for an expansion of this idea (sort of).
Perhaps this consideration would also apply to using particularly gruesome methods of torture when killing them. Just a thought. I would assume that if they are equally priced, it would be ideal to simply kill them in a less painful and mean way.