If you've seen a liquid cooler in an HP case like yours, it might fit easily enough. What I'm saying though is that if all you need is to have a quiter PC while keeping your CPU relatively cool, you don't need a liquid cooler, which is more expensive and takes more effort to install. To change the CPU cooler to a good air cooler, still involves you screwing in the new heatsink to your motherboard, which might mean removing the motherboard if there is no large opening in the backboard behind the CPU, so it's not going to be a five minute installation. And you'd need to make sure the cooler fits into your case in terms of height. Replacing the chassis fan at the back would be an easy five minute job, or similarly adding an intake fan to the front, if there is space for one. But just changing or adding chassis fans won't quarantee that your CPU will run much cooler than it is now.
You have a few options, change your CPU cooler to an air cooler, change it to a liquid cooler, or improve chassis airflow. Each one has many pros and cons. If you have a friend who could help you, perhaps they could have a look at your case and see what would fit into it, and see what the case airflow is like right now.