You can put the related field on a layout.
There are a number of visual tricks to hide the code beside or behind the related field.
One way is to add the arrow indicator to your field to hide/show the value list. Then shrink the field to just be the arrow and place it next to the related field for the description. I use this technique on data entry layouts on a report layout you can simply place the related fields on the layout anywhere.
It looks like you have been able to establish table occurances for your MySQL data in your FMP database so adding a relationship between the tables shouldnt be a problem.
You can place a copy of your category code field in your report header formatted as a pop up menu with a version of your value list that shows only the 2nd field. By setting a line width of zero for the field's borders you can conceal the standard "beveled block" look so that it displays like a normal field, but you'll see the 2nd field category name in place of the code.
Also, your relationship to this value table should have enabled you to just add the Category Name field from that table occurrence directly to your layout.