It is perfectly possible to write a VBA macro to do this. If you want the
macro to run automatically when the user click the printer icon, you give
the macro the name FilePrintDefault. It then runs instead of the built-in
Word command of the same name.

Now, such a macro isn't necessarily *simple*. How complex it is depends on a
variety of factors.

For instance, do you need to support more than one make & model of printer?
If so, you have to cope with the fact that different printers give different
tray ID numbers to their paper trays, and almost all the IDs do not match
the built-in constants offered for the purpose by VBA. This article explains
the gruesome details.

Controlling the Printer from Word VBA
Part 1: Using VBA to Select the Paper Tray
http://pubs.logicalexpressions.com/Pub0009/LPMArticle.asp?ID=101

Then there is the question of whether you are printing duplex. If you are,
then printing the first two pages of a letter onto the front and back of a
sheet of paper from one tray, and then the rest of the letter duplex from
paper from another tray is complex. If you just set the FirstPageTray and
OtherPagesTray properties to different trays, what happens is that page 1
gets printed single sided from the first tray, and page 2 starts on a fresh
sheet from the other tray. What you have to do is set both the FirstPageTray
and OtherPagesTray properties to the letterhead tray, print the first 2
pages, then set the OtherPagesTray to your other tray, and then print the
rest of the letter.