Stay away from HitBtc regardless of how small the amount is.
Not sure what's the source of your info, but binance doesn't have a strict KYC policy. If you're not from a banned country, you should be fine withdrawing up to 2 BTC per day without the need of verifying your identity.
And if you want another alternative, then Kucoin is a great one (same policy as binance).
Regarding HitBTC, will do, although like some others here I haven't had any negative experience with them and haven't heard about it. As for Binance, I read their Terms and Conditions and that's what I thought they meant here:
Your registration of an account with Binance will be deemed your agreement to provide required personal information for identity verification.
The information we require to verify your identity may include, but is not limited to, your name, email address, contact information, phone number, username, government-issued ID, date of birth, and other information collected during account registration. When providing the required information, you confirm it is true and accurate.
If they don't actually enforce KYC every time, then it might be a good place to start, although that right of theirs to distribute data to third parties is still disturbing.
I wouldn't suggest some random cryptocurrency exchanges but just one which I have been using and nothing bad has happened. Binance to me is the best exchange for anyone who want to trade bitcoin, their policies are easy going type unlike some crypto exchanges with fake policies. Stay safe with binance and trade to your satisfaction. Another cryptocurrency exchange I can vouch for is the Bitforex exchange, although I have traded some few times with them.
Yeah, I know that Binance is highly reputable, but their terms really don't disturb you?
Let me quote something from them:
Depending on the products or services concerned, your personal data may be disclosed to the following third parties:
third-party business partners who provide goods and services or sponsor contests or other promotional activities, whether or not in cooperation with us;
I guess for now, Binance does still sound like the best choice. I know it's easy to use, has favorable fees and probably the best reputation. I'll have my friend look into some other options mentioned here, like Kucoin.