Hi,
I see three choices:
1. Use tables: DON'T! It'll look ugly.
2. Use one of the latex packages for commutative diagrams like tikz or xymatrix via a TeXmacs plugin. DON'T! We want to avoid LaTeX, right? Also, I doubt those plugins have been maintained recently.
3. Use TeXmacs graphics.
Well, my suggestion is clear ;)
Insert->Image->Draw image will get you started. Remember that you can resize the canvas using A-Left, A-Down, etc. Use shift to go faster. Use the grid to snap your text, math and arrows, then hide it.
Once you have one diagram made, you can copy and paste the whole drawing anywhere in your document, and you can easily create a macro out of it, again copying and pasting.
If you want to go deeper, you can create a so-called "graphical macro". This would let you create and insert components for your commutative diagrams using the interface for the drawing tool and it's easier than it seems. To see what I mean, add the style package Experimental->graphical-macros to your document, then Insert a drawing and change the active tool by clicking on "Point" in the focus bar. You'll see new stuff there.
Hth,