I figured out how to do it.
In the current document, in the HEAD tag, type the following code (where href= refers to the different page you want to print without loading to the screen first):
<link rel="alternate" media="print" href="different_page.html" />
<script>
function printWindow(){
bV = parseInt(navigator.appVersion)
if (bV >= 4) window.print()
}
</script>
and then in the BODY of the current document type:
<a href="javascript
rintWindow()">Print The Different Page</a>
(I wanted a link to print and not a print button).
I know this won't work for every browser, but it will work for my purposes. Thanks to everyone who replied with suggestions!