You have to be careful here. Part of the reason the reputation isn't shown before monks vote on a node is so as not to influence the voting, as you say. If you can arbitrarily change your vote after casting it (with no penalty; I'm not sure how the form you suggest would work.) then this problem pops up, albeit on a much smaller scale.
First off if this misvoting is a serious concern, then it should be possible to at least print how you voted next to the rep. This could be done only immediately after the vote, unless the database is reworked to record each and every vote ever cast. (As opposed to currently, where I suspect it is only recorded that you voted, not how you voted, although this is only a suspicion.)
If in fact it is recorded how you vote, then changing a vote would be easier to implement, but you should be penalized if you decide to change your vote. Say by using up an extra vote to change an old vote. Additionally, some thought would have to be given to how this would affect the experience of the writer of the node in question.