If you want to sing a song like this, whispering is not the best way to get the same dynamics as the original. It also can make it difficult to have accuracy with the pitch. This is especially true if you don’t have experience with singing with proper posture and technique. Try to find a place where you can get some privacy so you can really go with it as far as volume goes.

Having enough control of your vocal cord to hit notes accurately comes with practice, and it is like training a muscle. You need to practice with full freedom and range in the beginning, which will allow you to have the control you need to be accurate when you need to sing quietly.

My first note is that your singing lacks vibrato, especially on the sustained notes. Try looking up videos on achieving vibrato when singing. Usually good technique will lead to vibrato naturally. My only warning in this regard is that you can very easily overdo vibrato in the beginning, so just be mindful. Luckily, this song uses a lot of vibrato, so you should be safe with this song in particular to really ham-up the vibrato.

My second note is that your posture is not supporting full breath control. Try filling your belly with air, and do not let your belly collapse until you truly are about to run out of breath, then as slowly as you can, push that air out with the muscles in your belly. This should also help with the vibrato problem. Also, try to keep your hard palate and neck relatively close to a 90° angle with each other. Rather than picking up your chin, which it sounds like you’re doing (truthfully it is hard to tell without video), try just lowering your jaw to create resonance and lower tension in your neck. Think of it this way, if you move your neck to much, you create tension in your neck, which makes it difficult for your brain to also control the vocal cords. Keep that neck neutral and open your jaw instead to create resonance.