Should I ask my coworker out on a date?
Go for what aligns with your values.
Right off the bat, I love this question for a few reasons. You are honest here. You can admit shortcomings in life. You see someone you like, admit that it might not work, and you also admit that you believe you should go for it.
Fear is a funny thing, right? Fear says you shouldn't do something because of this or that. Fear here says that you don't want to impede on her. You don't want to embarrass or upset her. Because this is a concern of yours, I can tell you, you won't have the effect you fear, mostly because you genuinely care about her. You admit that she could end up with someone else. Here's the kicker: You admit that you can at least say you tried even if she does not want to be with you.
My title was, "go with what aligns with your values" because when we make decisions based on attributes we want to see in ourselves and others, we cannot fail. We cannot truly fail if we follow-through on our authentic self, which here is to ask her out, despite all the fears. Remember this too, your mind secretes thoughts like the pancreas secretes bile. Thoughts are what your mind does, just allow them to exist and stop trying to challenge or deny or fix these thoughts. Let old thoughts that get your attention pass by like leaves on a stream.
You value being authentic and putting yourself in situations with others that you truly like and believe they like and could be good for you and you for them. You care about other people and think about them, which aligns with your values because you do these things. If you did not care about people, you would not consider these ideas.
If you do not ask, you will regret it. Think about you in five years. If you find some time machine and come back from five years in the future, what would you then tell you today? I highly doubt the older/wiser version of ourselves would ever come back to us today and say, "oh no, you shouldn't try; you should just put your nose down and admit defeat." Here's the bigger picture. Even if she says no. Even if she laughs, and says she feels uncomfortable (which is her issue and not yours), even if it ends horribly, you did something you can keep doing to start new habits.
How many times do people miss out on life because of stagnant beliefs or fears and don't even try to take a chance? People lay on their deathbeds and think about what could have been if only they had done the uncomfortable and challenging thing for a reward they really wanted. You, sir have the future you's possibility in your hand today. It is a lot of responsibility, but this power has been granted to you.
You need to do with the power as a responsible caregiver would do, and that is to act on the opportunity given. Ask her out, stand there and see what she does. Don't get lost in your head, be present. Focus on the bottoms of your feet and stay grounded in all the awkwardness that is the moment. If she indicates discomfort, that is her issue and not yours to remedy. You could end up making an impact on her life as well, all the while living for what you care about.