You have two problems, money exchange commissions and currency risk.
Commissions are always exorbitant.
First you must find the cheapest way to get your money converted to the foreign currency and into your brokerage account. The absolute cheapest way may involve some research and financial institution maneuvering.
Also I'd forget about anything other than USD for the foreseeable future. Any other foreign currency will probably have higher commissions and a weaker market.
Once you have that down, you must avoid needlessly exchanging currencies. Keep a balance in the foreign currency, keep all dividends and capital gains there, and only take local money out of your brokerage account right before using it.
That means of course that you need to keep enough local currency to pay taxes on any gains, etc.
As for currency risk, there are two solutions.
One solution is to buy your risk away using forex. You sell an amount of USD/AED lots that is mostly equivalent to your current investments and then just make sure you don't get margin calls. I'm not sure just how cheap your rates would be in the UAE, but, on average, your investments should still have positive returns.
The other solution is to just stop seeing exchange rate fluctuations as losses. If you had USD 100k and now you have USD 115k how are you losing money? Exchange rates can go the other way just fine, you know, and holding USD is a good way to hedge against your country going south.