Both 享受 and 欣赏 are types of enjoy, and they do have different meanings and should be used in different context.
享受 can be though more of receiving an enjoyment, such as being pampered. It is often used when someone or something allows you to have your enjoyment.
欣赏 on the other hand is more of an admiration towards other things. For example, you can admire a piece of artwork, and enjoy the artwork.
In your sentence, you picked 享受 correctly, as you are not admiring anything in this context, but simply receiving from the trip/vacation. However, I would use 无法 over 不会. While in English, I won't sounds perfectly fine, in Mandarin, it sounds like you won't because you don't want to. If you said you can't instead of you won't, people will feel you are more polite and relate the cause to the lack of sleep instead of you not wanting to make an effort to enjoy the trip.