You can certainly export everything even if it is all just organised in map view, but one of the key things with Tinderbox is that the map view does not impact outline order. In your case, this is going to be a frustration most likely, but generally it is considered a feature.

Moving a note spatially above another note (or from left to right) does nothing to actually re-order the note in the outline. It would be too difficult for Tinderbox to try and guess what you mean by the movement. So if you have never organised anything in the outliner, you might find it is a huge mess.
Depending on how you have things organised, you could
maybe sort the map container by Xpos or Ypos---but I'm guessing you probably have clusters of notes where a super-cluster (Act I) might be organised top-down from the next super-cluster, but within the cluster everything is left-right or even in a matrix. In that case, a simple sort will not work.
You could try sorting by Xpos first, and then Ypos second (or the other way around if the case may be) and see if that gets you close enough to save an hour.
Going forward, a good rule of thumb is: If you intend to export in a linear fashion where order is important, then working in Outline and using Map as embellishment is the direction to go. For example, when I was working on a book in Tinderbox, I had things organised primarily by plot thread containers, and then I would drag manually created aliases into chapter containers which were organised in act containers. So there was one part of the outline that I could export in a linear book-order fashion, and another part that had all of the plot threads in their own order which I could export to check for continuity. I used maps within the book-order container to keep track of non-order related details.
So what I would do is create a structure like this:
Code:- Book
- Act I
- Act II
- Act III
Then select everything in the Act I adornment and drag it into the new Act I container. Likewise for the rest. Then as already suggested, use the existing spatial map as a reference to organise everything within those new containers into book-order. If sorting by Xpos+Ypos gets you close, do that before you drag notes. Use colours (if you aren't already) to make sure that everything is grouped together as it should be in the outline. By that I mean, select everything in Act I and make it bright red in the Color menu. In the Outline view, you'll see where all of those notes actually are in the Outliner. Then play with sort until everything is grouped together. You might have some other attribute that is more useful. Say if you have titled everything numerically "1. This is chapter one"---then obviously sorting by name would be useful.
If sort doesn't work out, you'll just have to do it fully manually. With 100 notes, it shouldn't take longer than an hour or so.
Once you get everything organised into the proper book-order, select the "Book" container, create a Nakakoji view, make sure "Book and contents" is selected on the left, and choose an appropriate export template. The default will just give you an indented and numbered outline. Then export and you'll have a file ready for print.