It depends what you mean by "hands on".
If you want to fix aeroplanes, don't do a degree, it's a waste of time, money and energy.
There are however plenty of people with degrees who are for example spending their lives in a lab - designing and testing equipment prototypes, wind tunnel testing models, managing trials. I spent quite a few years in a flying suit, using what I learned on my degree sat with a Test Pilot, managing flight trials - I certainly didn't anticipate when I graduated in 1992 that by 1995 I'd be earning part of my living strapped into a fast jet, and some of working on an aircraft carrier.
On the other hand, there are also plenty of people with degrees who spend their life sat at a desk in front of a computer, and a proportion of people with licences who do the same.
If you don't want to sit at a desk much, then your best bet is an apprenticeship, but research lab work is one of the things a degree can get you into, and can be incredibly rewarding - and certainly rarely involves sitting at a desk or wearing a suit.
Engineers with a degree and a lot of practical experience probably do have the best choice of jobs. They've also spent a lot of years studying, and that's not to everybody's taste - either a licence or a degree will take 4+ years, and then you need experience as well as your degree/licence before you have much choice of jobs or a decent salary. In either case, you really need to WANT to work in this industry, just to see your way through the training.
An apprenticeship with Rolls or Marshalls should put you very hands on - mostly in build or maintenance. There will be options if you do well to switch to management or labwork, the latter particularly at Rolls. I can think of worse jobs than testing prototype jet engines.
G