That's why I'm using XRP when I withdraw to this site, and just convert that xrp to btc in my local exchange.
Since, AFAIK, yobit has a very small charge on XRP withdrawals, it's less than 1 XRP but even if hitbtc charge 6 IIRC, it's still cheap since XRP's price now is cheap.
In dealing with high fees then theres no other possible way to reduce or get rid of of high fees but making up some conversion to other alts which do have very cheap fees and this is also my way when i do encounter such scenario but hitbtc and yobit are shitty exchange that doesnt even bother to adjust their fees and set it out on stone which would really scare out their users that do decide to make withdrawals directly with btc.
This is no shocker and Hitbtc is been known with some issues not only into its fees but on other things well but there are still people who do deal or make use of this place but for me, ive long time avoid this one.