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That's why I have a dedicated laptop just being used for my bitcoin activity only. (sig campaigns, trading) and I don't download anything. Just my anti-virus to go and firewall. Just sad though, that you don't have a slight suspicion that someone is harnessing your CPU for their own benefit. We need to be careful anything from the net, specially about crypto's because it is taking the world by storm and everyone one to take a slice of the pie.
I dont think you are cautious enough. If you have 2 computers then use one just for wallets you trust 100%. Nothing else. And another computer for everything else, including some new coins signature campaigns where you download their wallets, that can actually be a malware. But since you have nothing valuable in any other wallet on this computer you are perfectly safe.
We do not need two computers you only need one with a safe and verified OS then you install in an external hard drive all your wallets and after you do that disconnect it, now your wallets are in cold storage and you can use your computer for everything else, if you can afford several computers then you can use your method but it is cheaper to just buy an external hard drive or if there is not a lot of money in hand an USB may be enough.