0.93.3 is fine for at least another couple years.
Maybe not fine, but certainly safe. If unmaintained, it is only a matter of time before it can no longer send money unaided, after some soft or hardfork has made it necessary to update bitcoin core to a version Armory cannot communicate with. But in that case, you can always export the private keys and import them in another wallet.
Of course after a few years you may need to dig out an old linux distribution and run it in a VM to even run Armory, but while tedious I cannot see how that could stop working.
I am not worried yet. But of course I am considering other options (electrum) if goatpig does not succeed in carrying on the torch.
Unless ECC, SHA256 or AES is broken in the future, Armory is safe indeed. And the internet as a whole would be in a lot more trouble than just Armory if that were to happen.
When I said fine I meant fine with regards to Armory's reliance upon a local Bitcoin node. 0.93.3 can't make sense of SegWit transactions, it will just ignore them. It can still spend coins that are not "SW'd". There would an issue in receiving SW transactions, but the idea here is to move coins out, not use the wallet for actual trading.
Generally, if you used Armory in the past for your cold storage, you can expect to be able to spend those coins with Armory as long as no hard fork has been deployed modifying the legacy Bitcoin transaction rules. If the changes are done through a soft fork though, you should be able to spend just fine. I don't personally expect the network will go through a hard fork that would break old style Bitcoin transactions for next 2-3 years. There are plenty talks of hard forks lately, but I don't believe any of those are meant to change on chain transaction structure. I could be wrong though, but again, I expect the network to prefer soft forks whenever possible.
Anti malleability changes like lowS would reduce Armory's usability, but with some persistence, it would eventually create a valid transaction. Block size hard forks are irrelevant to Armory, but changing magic word within the block files would break it. However, fixing that is a matter of changing one hard coded line within 0.93, nothing too dramatic.
Changes to the raw block data saving formats will stop Armory. So far, changes of that category are pruning and obfuscation. Both these features can be disabled and if you find yourself 5 years from now trying to spend old coins with 0.93, you should be disabling that stuff anyways.
As for running the binary, I don't see why you wouldn't be able to build from source on a Debian distro 5 years from now.