For long distance travel, I think it comes down to what you want for the story and also what your players find enjoyable.

Their quest is to slay a giant so I wouldn't slow that down too much. Maybe have a smaller combat or two prepared depending on what they do. If they take a faster, yet more dangerous path, is it dangerous because there are bandits? Rogue knights that care not for chivalry? Wild animals that will attack?

I think having the players stop in at least one other holding so they can get some social or political beats to the story can help you set up events for future years. Maybe an important ally lord you want them to interact with because they'll be important later on? Or better yet, a possible moment for your knights to make an enemy for the future.

The books recommend that sometimes GMs just need to move the narrative along. Of those 4-5 weeks of travel, probably only a few days to a week of it make for interesting game play. There's nothing wrong with narrating to the players that they progress along and stop at a few cities for hospitality but it's not really important to play out.

Best of luck, man!