I want to send some coins from my Windows wallet to my Ubuntu wallet. Both are based on nodes using the latest version of core. I'm not bothered about confirmation times, even if it takes a week to get a confirmation. It seems that no-fee transactions may be possible under certain circumstances.
Historic rules for free transactions
A transaction was safe to send without fees if these conditions were met:
It is smaller than 1,000 bytes.
All outputs are 0.01 BTC or larger.
Its priority is large enough (see above)
The above quote is from the Bitcoin Wiki.
Another quote is
The reference client currently refuses to relay transactions it considers unacceptable, such as those with zero or no fees. However, there may be miners who are willing to put these in a block. This group is for people who want to send such transactions, and those who want to put them in blocks.
To participate, have your node maintain a connection to Lightfoot Hosting's node, which relays indiscriminately. This means that you can broadcast your transaction to it, and it will relay it to any miner who also has a connection to it. If your transaction meets the policies of at least one miner connected, it should eventually be mined into a block.
Are these two quotes still true. or are no-fee transactions dead in the current market?
Transaction priority was always just node policy (i.e. not a consensus rule). As fees become more relevant, rational miners care only about confirming transactions that pay the highest possible fees. So most (if not all) miners have removed the policy (which reserved space for priority transactions). Since apparently no one was using the policy anymore, Core removed priority from its fee estimation.
So, the answer is right on the wiki page you quoted:
almost all miners expect every transaction to include a fee.
Technically, miners can include whatever transactions they want in the blocks they mine. That's basically their only power. Rationally, it doesn't make sense to publish no-fee transactions. But I've seen zero-fee transactions confirmed in the past few months, so I know it happens. The circumstances of those transactions? I can't say. Maybe they used an accelerator service. Maybe there are still some altruistic miners or pool operators out there.