The short answer is no, you cannot prevent users from seeing the option in their browser using just javascript.
The slightly-longer answer, is that you can do this with a bit more than javascript.
Using a service such as html2canvas, you can send a POST request to a page on your server. Use that page to convert the image to a PDF, and have it output the file as a download.
Assuming you're using PHP:
<?php
header("Content-type:application/pdf");
header("Content-Disposition:attachment;filename='screen-shot.pdf'");
// The above headers will cause the file to automatically be downloaded.
// Use a library to convert the image to a PDF here.
An example library to convert an image to a PDF is mPDF, or TCPDF. Feel free to Google others, especially if you're not using PHP.
Do note that this solution is inferior to them just making the choice themselves, as the quality definitely won't be as nice.