Can I back-up an installation of my Photoshop?

Hi folks- here is a question for you: can I back-up an installation of Photoshop CS3 which I have installed to my MacBook Pro 2.3 GHz Intel Core i7 running OSX10.9.5 so that I can start over?

Background to the query: I had to buy a new MacBook Pro just under a year ago but install my older MacBook Pro's data in a hurry and did it wrong. This means that Mavericks, which had a user set up for this new machine received the old user as well and did its best to marry the two but, as you can imagine, it's a bit of a mess.

In my defence- I didn't heed everyone's advice to start over properly before it got too involved but felt I couldn't. I had lost the hard drive of the old MacBook Pro at a bad time, was under time pressure, and had no time to "learn" new tricks (I was worried that the installations of other software would be too difficult to do).

I discovered that certain software would not run on Mavericks and I couldn't downgrade the MacBook Pro to Snow Leopard (still my favourite OS) so began reacquisition... And after much searching and bidding unsuccessfully managed to buy the minimum to run on Mavericks, ie a full retail version of Photoshop CS3 which came with EVERYTHING and was allegedly deregistered.

Only- it wasn't. I had the wonderful support from a lady at Adobe who overrode the problem and advised me to not uninstall it as that would just get me back to square one, ie that I had the physical disk, box, paperwork with serial number but it was still registered to someone other than myself (and before you ask- no, not the seller!) and I'd not get it installed again. Since I cannot guarantee that I'd get her or anyone so nice again- I'd hesitate to chance it.

Why now: I have a little down-time now and some of my other software is a tad wary of a system which is pretty Jekyll and Hyde so thought to do my research.

Recap of question: Ideally I'd move the Photoshop CS3 installation to an external hard drive and then reformat the MacBook Pro from scratch and move the the installation back across. Is this a pipe-dream or is there some way of doing it?