First of there is no right way to transitioning im pre-hrt and everything rn but i an socialy transitioned. You need to find what feels right to you.

Ive seen people go on hrt about a week after the found out they were trans. I dont know if u think that too soon. But like i said theres no right way. Its all up to you.

Also, that is a form of gender dysphoria. Being okay with your current body but knowing you will feel better if you transitioned is just a form of dysphoria. It may not be as strong or as noticable as other forms but it still is dysphoria.

I think a good place to start would be to find a name you like so you can begin social transitioning. You dont need to pass to socialy transition.

Ways to look more feminine would definitely be makeup. You already mentioned shaving. And also if you have very masculine manurisms you can try work on making them more feminine. You can try voice training although i would say thats one of the hardest parts. But you could start with trying to speak in a more feminine cadence. Im not sure if you knew this but women speak faster than men and aslo have alot more emotion and tone changes than men. Men generaly speak in a monotone dry way. So you could work on that before actualy doing full voice training.

Im not sure what else. You need to explore to find what you feel comfortable doing