Can't you sign a message? It doesn't need WiFi and won't affect your privacy. Just sign a message from that wallet, post signed message here and we will confirm whether you are real or fake.
If you want a tutorial about how to sign a message from Electrum, here it is, check this image: https://imgur.com/qXbURuy

Now, let's talk about the concerns you have. Can you redeem your Bitcoins? Well, keep in mind that blockchain is public and governments are getting advanced in blockchain analysis. This wallet is very hard to not notice, so keep in mind that all eyes are on you in case you move coins from it. Also, keep in mind that news websites like Cointelegraph, Coindesk and others will publish articles about how Bitcoins moved from one of the famous Bitcoin address that belonged to Mt Gox.
If you really do have access to those Bitcoins, then don't do a thing without doing a very deep research about how to protect your privacy.
Good Luck