I understand that something like MEW is necessary but still makes me paranoid that a lot of my information is going through a third party.
I don't know how things works with Algorand, but i want to note that MEW is not a third part entity. It's an interface that let you interact with Ethereum network through your web browser. There is no servers or stored logs. I can't say it's totally safe, but it's almost secure if you have enough knowledge on how to use it.
I'm not that tech savvy to know the exact nature of the process of transferring assets between the ETH network and Nano via MEW, BUT my educated guess would be that there has to be some data transferred among all three parties. I'm not saying that MEW is suspect here, I'm saying that it is a third party though. By its very nature of being the go between as an interface.
MEW has to access your hard wallet at some point during the transfer process doesn't it? There has to be some communication going on there.