See my title. I am looking for a word or expression to replace the way of "Shall I/we ...?" The context is I am asking for permission or suggestion but it is not in conversation. I want to apply such sentence in written English. The dictionary says, that is the spoken English.
I'm not sure which dictionary would suggest that shall is only used in spoken English, but I have to assure you that it is perfectly fine to use it in written English too, especially in literature.
If you are still looking for a replacement for an expression that involves the usage of shall, you would have to first determine what it truly means in the expression:
My guess is that you are using its fourth definition. In this case, you can simply rephrase the sentence this way.