It's difficult to reply to this without saying 'I told you so', or 'what were you thinking longterm'.
Passengers look upon their pilots as skygods. They know nothing about aviation and rely on the guys up front to get them safely from A-B. They have an idea of what their pilots will look like, just as I have a conception of what my (good) doctor, dentist, lawyer and accountant will look like before I meet them. This preconception will be different from what I expect a courageous young officer will look like leading a platoon in a war torn part of the globe.
The people interviewing new airline recruits will be older than you with those preconceived conservative values entrenched. I speak of western Europe only but I can imagine the mid and far east to be similar. The HR people drink conservatism on a daily basis and I'm afraid that isn't gonna change for a quite a while.
If you really can't get rid of all your tattoos then I believe you should consider carefully your career in aviation. You'll be spending a lot of money to become qualified and then you'll buy a lottery ticket trying to get a job. It's so competitive nowadays that any impediment - seemingly as trivial as taking two attempts at some exams, having a minor restriction (OML 'as or with a co-pilot') on your Class 1 medical or a just visible tattoo - will put you in the DCM pile. (Dont Come Monday).
Wearing a long sleeved shirt I don't believe will cut it either. What happens when you go to the pool for your first dinghy drill? Everyone in speedos and you in a boiler suit! Even though you have an unrestricted Class 1 medical and have the job offer, what will the company doc say when you attend your initial company medical that every new employee has to attend. (This may not be the case with every employer but your blood pressure will ramp up when you've almost got through the door to find that this employer requires a medical checkup).
Life is seldom fair and I know this is a form of discrimination. With your drive and determination you'll probably make a good pilot, but it will be difficult to live with the glass ceiling that your colleagues pass through while you're limited in the opportunities that you can apply for with your 'impediment'.
There will be other takes on this conundrum, probably telling you to ignore the old fart. Problem is it's the old farts than run the companies and make policy
I wish you luck.