I have a thief like character, who needs to climb over a wall. No rope, ladder, or other such tools. How would he potentially get over the wall without outside assistance. He needs to leave no trace from a rope, ladder, etc. I was thinking about having him use daggers to stick into the wall and climb, maybe somehow attach them to the fingertips of gloves.
Take a look at Alex Honnald.
With the right level of skill, anyone can climb nearly anything. Here's what the Rhodes medieval walls look like in Greece:
As you can see, plenty of hand holds there. But not all walls are going to be the same.
In Spain for instance, there's this:
These walls are worked so that the mortar is even with the stone, so it would be difficult to get a hand hold, and in fact, a lot of the Spanish walls were built this way.
I'd say your climber is going to be able to handle most medieval walls if he's skilled enough, but there's just enough variation that, well, not all walls are created equal.
As Brythan suggested, even then, corners and curves in design can make things easier. None of it is impossible at a high skill level!
You do not want to give your climber gloves with blades on. I have climbed in the past myself and I can tell you that a bare hand is the best tool you can have, along with a pouch of chalk at your belt to keep your hands dry.
One thing I have noticed with novice climbers is this: in general women tend to do better than men. At higher levels guys can outstrip the ladies, but ladies are better to begin with for a couple of reasons.
We don't rely on upper body strength to solve problems. Guys tend to as a default because they HAVE upper body strength, so they make the mistake of using their arms to pull themselves up rather than using their legs to push themselves up. This leads to muscle fatigue fairly quickly. Novice women climbers chose their handholds really carefully as well, thinking things through a few more steps ahead, while the novice guys tend to get cocky and stuck in a bad spot more often. Upper body strength and grip is important but you've really got to choose when you use it and let your legs do most of the work. That way when you really do need the upper body you can use it and your muscles won't be fatigued. Overall, women have less lower body strength than men, but because they rely on it more, to begin with anyway, they are better climbers. At higher levels of skill, men far outstrip the ladies.
First, most medieval walls are going to be rough enough that a good climber can just climb them. That is to say that they are similar to a cliff face, with enough holds to allow climbing.
Even if we assume that your thief cannot do that. Look for narrow chimney-like spaces created by the fortifications. It's possible to climb those even without handholds. Some tips from rock climbing. The basic idea is to use pressure to maintain height and shift position frequently.
I'm not convinced that knife blades in gloves is what you want. Knife blades in boots makes more sense to me. Carrying actual daggers in one's hands makes more sense to me than trying to put small, breakable blades at the end of one's fingers. Or even better, use picks that are tied to your belt by a slack rope. That said, most rock climbers go the other way and wear thin footwear and thin or fingerless gloves so as to be able to better feel the rocks.
Run up the wall.
This dude runs up a wall that I estimate to be 20 feet high. I am impressed.
Here is a tutorial on how to do it; this wall running is a parkour move. https://parkour.wonderhowto.com/how-to/do-tricky-wall-up-wall-climb-parkour-move-377108/
Spring Heel Jack style would work, never found a concrete trace of the guy
Just leap over the wall.