To be totally honest, if you do not have full access to your coins (private keys) you are taking risks. Don't use online wallets. Use a wallet that is physically on your computer or on your smart phone for the Bitcoin that you want to be using, and cold storage (like a paper wallet) for your savings.
Sometime online wallets become essential while travelling. I think op mentions using one for only small amounts.
So this shouldnt be a problem here.