For my answer, I am basing it off of the following link
Lost Clan Schools
Yes, You Risk Losing Honor
Pure RAW, it is a low skill use. Nothing in the School's description mentions honor loss from using intimidate or any low skill. However, you start with 2.5 honor, and none of the school abilities seem to be rooted in your honor. According to the honor loss/gains chart, using a low skill with a 2 Honor is only a -1. When combined with the Rank 5 ability, that -1 Honor also helps bump your initiative to +15, +25 if you centered the round before (re: iaijutsu).
The Loss May Not Qualify
The description of the ability sounds like the Jirozame in question just gets "ice water in their veins". Their intimidation factor comes from clearing their mind and being ready to attack without hesitation, which shakes their opponent, and not to bully or torture people. In combat, especially when it's openly declared or an iaijutsu duel, there are certain exceptions to what is considered "honorable".
My Personal Take
It would seem to be a weak rank 2 ability to lose honor for +5 init when you still have to make a roll for it to succeed. As stated in another answer, GM caveat would probably let you get away without the Honor loss (or forget). Comparing to something like the Matsu Berserker Rank 2, which requires a hit for damage then a target declaration, then they get a willpower roll and they can't use move actions until their next Reaction. Although the the technique does work best when picking on weaker opponents (low willpower, Honor), which could be considered a loss of Honor anyway based on circumstances. The biggest catch (hah) to me is how this applies in anything but single combat. Once again moving to GM caveat, but I feel like this would have been better served as "pick an opponent and give them -5", but that's not what's in dispute today.