By the same reasoning, what if the entire Bitcoin network is consisted of honey pots?
Then run your own node. No one knows which addresses you are looking up for balances, since you are looking them up locally.
Broadcasting through a block chain explorer is a solution, however I'm sure you can send it directly to the network, without this kind of site-intermediary.
All these sites are doing is broadcasting the transaction via their own node. If you are going to use someone else's node, then you are always going to have to go through them (or some other third party) to do it. If you don't want to do that, then the only remaining option is to run your own node.