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I have not checked all responses above, but with someone with their OWN computer could use Wifi (in hotels, coffee shops, etc.) by using TOR (free) and/or VPN (not expensive) and be pretty secure, especially with a hardware wallet.
The above is not "Rocket Science", if I can learn to do the above, almost anyone else can.
I wonder if OP had already use those? I mean that's the first thing we should use and why using public internet cafes seems the last resort for him? Don't he have phone?
Don't take the chances, maybe now your wallet is safe but the moment hackers track it, it's the end of the story. Hackers are clever and persistent tho.
Yeah. It's a bit weird for sure, I'd like to see reasonings for this, most popular online wallets (coinbase, blockchain.info, coinjar) already have pretty popular and working wallets on their apps.
One thing I could think of is that it's a paper wallet? But there are apps, electrum for example that let you install it on your phone.
Most internet cafes in my area have those features, sorry for any confusion.