In 他是一个不负责的人，（要／想） 当我们的经理, does it matter if I use 要 or 想?
You should use the word "想" in this case. I think the sentence you're trying to write is:

He is an irresponsible person, he thinks he is our boss / manager.

Using the word "要" in this context speaking about an "irresponsible person" doesn't make sense.