Be careful about "don't bother", it can be interpreted as actively hostile.
It's about like when you say to your other half, "I'm going to spend the rent for the next 3 months on a new motorbike", and she (sorry, it's usually "she" in this context) says "Fine!" when she really does not mean "fine", what she means is "I'm obviously not going to be able to stop you doing whatever immature selfish thing you like, but if you do, then our relationship is over."
In this case, "Don't bother" means "It's obviously far too much trouble for you to just perform this minor courtesy for me, and I clearly cannot rely on you to pull your weight in this relationship, so please be aware that our relationship is on shaky ground as of now."
So if someone offers to wait for you, and you say "Don't bother", it can be interpreted as a rude rejection of a courtesy offered, and the person asking would spend considerable emotional energy wondering what it is that he or she has done to upset you.
Better would be:
"Thanks, but you go on ahead, I'll catch you up later."
Then there is nothing in what you said that indicates that there is any sort of obligation that you need to be waited for.
Even saying "thanks, but you don't have to" is using the language of obligation and duty ("Have to") and can cause awkwardness.
"Warm wishes" has connotations of "very friendly" or "with love". It is an expression that you might see in a note between close friends or relatives. In other words, the people who are likely to come to a modest birthday party.
"Kind wishes" is still very positive, but does not have the intimate connotations of "warm wishes".
"Wishes" is usually positive.
Best Answer
Neither of these phrases are appropriate for what you are trying to express.
To fool someone means to deceive them, so saying that you "fool yourself" would mean that you are tricking yourself into believing something that is false.
The phrase "fake myself" sounds odd. It would be better to describe the state that is being falsified, e.g. "fake confidence."
In my opinion, other words are better used to describe this situation, many of which you used in the body of your question. The verb "act" implies that one is faking. To say that you are "hiding" your true emotions is also a valid way to express this. Here are some more suggestions:
(Note that "pretend" is used as an adjective in my last example.)
Another word you might consider is "feign", as in "to feign confidence".