Converting a Pirated Copy to an Original

I know this might be a sensitive topic, but I'm an old school gamer who grew up playing games like Doom where you could play the first act free before deciding to purchase the whole game. When I see a new game I want to try out, I usually download a pirated copy (I'm a web & graphic designer by profession, so I can relatively protect myself from all the malware that potentially might be on these versions) to test it out. With DA:I, I did the same thing - liked it - but I still had a backlog of games(it happens when you have a full time job + overtime) to finish that I decided that purchasing this wasn't my first priority. Left the pirated game files on this computer, and played through my (legitimately-purchased) cache of games until I finally had time to get this game.

Fast forward to a few weeks ago, finished my backlog and now - ready to purchase and play DA:I. I bought the game (the sale price was a good reward for me waiting by the way) on my desktop and downloaded it there. Been having a blast so far, but I do some occasional travelling and I wanted to be able to install it on my laptop.

My laptop has the pirated version of DA:I.

My question is there a shortcut I can use to run the legitimate version of DA:I on my laptop without downloading almost 30GB again? 

Thanks and sorry for the long-winded post.