So he needed a horse because he WASNT in a rush. There would've been a way to break through sooner if he used magic, but a horse let him get to a secluded area without looking strong.
And since he so obviously wasted money on charity, for them to go through with it made it unlikely the assassins were anyone worth keeping alive.
You're sourcing this from a WN/LN or something?
I mean, things happened alright, but come on.
Do you remember last chapter then? He noticed that their chambers have poor airflow. When he rose from bed last morning, he farted in the farthest corner of the room. Hours later when the princess entered said room during the commotion, her nostrils were irritated by the smell of rotting eggs, which made her annoyed and less composed than she would be otherwise. Thus, she allowed him to leave. Unbeknownst to the princess, negative pressure produced when she opened the door, sucked just enough of the room's air and allowed for the smell to travel from the corner in the right moment. This also prevented him the embarrassment of young girls finding out he dealt it, sparing him from the fate of being called "eggy ojisan" in the future. That was my favourite part.