Hi Kathie,
I'm not aware of a style setting that applies only when printing, other than those you can set for the Page Header and Page Footer, which are the only elements that are editable in Print Setup.
Here you can set a style for a line separating the Header or Footer from the rest of the page (as I've done for the Header below), and the usual style settings for the text in the header or footer:
The column separators in the second copy of the table (2-1) were set using the Cell format Inspector in the document itself, and are visible while working on the document as well as in Print Setup, and in the printed version.
Description below.

Table 2
Selected cells B2-E6
Opened Format Inspector. Chose Cell.
Selected the 'all borders' button in the Cell Inspector, then set the pop-up menus to the right to Border Styles and No Border, giving the result shown in Table 2 in Print Setup above.
Table 2-1
This is a duplicate of Table 2, made after setting No Borders on the cells selected above. It shows the result the process is heading toward.
After clearing all the borders, it's time to put back the vertical ones.
As can be seen in the image below, there isn't a button for 'all vertical', just for right or left. And Right or left in this case means the right or left border of 'the group of cells'.

Here, in Table 2, I've selected cells E2-E6, then selected the Right button in the Cell inspector.
I clicked on the Border Styles pop-up and selected 3 pt solid black as the style to apply to this border.
Because the style is attached to the individual cells, it is included if we Copy Style.
BUT note that copying the Style includes copying the Format of any data in the cell(s) as well.
This could play havoc if you have mixed data types in these cells, or if you have the same data types
with variations in format through the set.
My sample is all text, and all has the same default format, so I can use Copy Style (option-command-C) to copy the style of one or a column of cells, then Paste Style (option-command-V) to paste that style into another column of cells. Note that as the Right border format applies to the right border of the selected group, I will need to select each column in turn, then paste.
Here's the result after selecting cell E2 ( "way" ), copying its style, then doing three rounds of select, paste style on the target cells in columns D, C and B respectively.

Finally, with B2-B6 selected, choose the Left button in the Inspector, then choose the same Border Style from the pop-up to add the left border to column A, completing the table as shown in Table 2-1 above.
You will probably want to choose lighter borders than the 3 pt ones I used.
Regards,
Barry
PS to Wayne: On posting, I noticed your shortcut—selecting all three vertical border buttons at the same time! Good one. I hadn't tried that.
B