@heroic,
@akthrowaiz,
@0TheWatcher0, @saitho514,
Let's not pretend that the only reason the MC didn't list, at the very least, Power Strike, Restraint, and Heal is because the author wants to make everyone surprised when the latter is revealed. It has very little to do with showing that the MC is being smart. It's the same silly logic that got him in this situation in the first place, the logic that the MC used to not go to the Hunter's Association early on and get this all over with. The same logic that had him out illegal hunting that's obviously going to come up later and get him in a situation just like MC just admitted that if they find out he lied about his skills later then he'll be in some trouble. The author is either going to use that to create a situation or throw it away with some authority figure who decides to favor MC just like the author threw away the examination by bringing in an authority figure to hand-wave the need for MC to take the test to make him seem more "special" despite us already knowing that he's unique while all of the characters in the story, or I should say most of them will think MC is weak. It's the usual trope that MC appears weak based on whatever system is rating him but is strong in reality.
@akthrowaiz makes a good point that his healing ability alone would give him some status given the lore we've already been given about healing abilities. He could also learn from someone who has one if that's a thing in the Association, we don't know yet if training under a mentor for a skill that mentor might have is also a thing.
@heroic, With his level being so low per the examiner, I doubt him choosing battle-related skills will work out the way you're saying.
Ultimately, this is just a fulfillment of the story's title, "Level Up Alone" because the author has an obligation to force this on the MC and seems to think, like so many readers, that it's best to make him hide a bunch of stuff and make silly decisions (like illegal hunting and selling on the black market without doing any research whatsoever). At the very least, if he was going to hunt solo and illegally, he should've focused on upgrading his stats a bit better so he wouldn't end up as a low class hunter which is obviously going to make things harder for him as far as staying under the radar, IMO. What happens when he starts to achieve things and people are going to be like, "you're an F-class hunter, how did you do that?" So the whole hiding stuff becomes moot as it always does in these types of stories. So there really isn't any significant logic behind it on the MC's part. It's all the author forcing the issue so later on he can make the MC seem that much more "special" when everyone finds out he has this skill and that skill and don't think for a second that everyone won't find out, they always do. Again, making the whole hiding it moot. Even when they find out there will be someone who wants to investigate, wants to study him, etc. The only difference will be at that point he'll be stronger so he could likely resist easier.