He has a completely valid argument—Friday can be excluded (that wouldn't be a surprise), Thursday can be excluded (since he already excluded Friday, it wouldn't be a surprise), and so on, until the last day left is Monday. So he can conclude the execution must be on that day.
(In fact, he has a valid argument for anything he might want to believe since the original statement made by the judge is self-contradictory.)
So now I'm thinking you're wrong because the logic that leads to excluding Tues-Fri can't also be used to exclude Mon. He can't expect execution on Monday and expect to be surprise executed on Monday.
When he inducts to Monday and then doesn't get executed Monday, he can't expect to use the same logic the induct Tuesday. Which means any day then becomes a surprise. He has a 1/3 chance (since we exlude Friday) of randomly choosing the right day, but no reason to not be surprised on any day except Friday.
(In fact, he has a valid argument for anything he might want to believe since the original statement made by the judge is self-contradictory.)