[support] URL Alias with Argument

My store 'category page' needs to show a list of subcategories, each with an image and text. I have taxonomy image and I wrote a bit of PHP on a page to create EXACTLY what I need.

The only drawback is that the URL is /node/7/x where x is the category id. I would like to use of course /cat/x but I don't see a way to do this.

I know that I in theory could have used Views to create the page in the first place, but I didn't see easily how to do this (including the taxonomy image) nor am I an expert in Views.

So is there a way to achieve a URL alias with an argument? I don't want to enter each one /cat/1 /cat/2 manually. :(

Thanks!