60 years ago there were no transistors, and portable radios and things had to use tubes. In fact when we refer to the high boltage for the tubes as "B" voltage it is a term left over from the battery days. The B battery was the high voltage one. The A battery for the heaters, and the C battery for the bias.
50 years ago I used to work on some of those radios. A portable radio was the size of a workman's lunchbox and half of that space was battery.
I see two directions you could go. You could go for a modern design using current production parts, as if you could go into production on the product if you wanted. The other direction would be to build a one-off using old parts and not caring if any more duplicates could be built - just a proof of concept project.
The main drawback I see is heater current - a typical small tube wants about 2 watts per heater. A power tube more like 5-10 watts. That is a lot from a battery in anything like portable size. Of course if convenient size is no issue then go old school with mutliple batteries. In the old days they made tubes specifically for battery operation. Tubes with low voltage heaters and lower current heaters. They also developed lines of super-miniature tubes for portable equipment and car radios. They developed tubes that didn;t need high voltage as well.
Then we used 45-60-90 volt batteries, but now we can make efficient compact switching supplies instead. A switcher for B+ is perfect. Other than the power tube for driving a speaker, the B+ voltage could be even higher than 90v if you wanted. Not a lot of current through preamp tubes.
I don't know where I put it but somewhere I have a survey of sub-miniature tubes I did for a project. RCA really didn;t get into that much, but the GE tube book is full of them. www.tubesandmore.com has many of them at reasonable prices.
SOme are shaped like a 12AX7 but half the diameter, and have pins for small sockets. But there are smaller ones still that look like an overgrown NE2 lamp - bare glass bulb with a row of maybe 5 wires coming out the end. They were soldered in place. These were small, like T2 or T3 bulb, maybe 9-10mm diameter.
Look up 6AK4, a little triode. Look up 2E35, 2E36. little power pentodes - we are talking milliwatts here though. 6BF7 twin triode.
6286 is a tiny triode - 1.25v heater @.14A
7963 twin triode
6021 twin triode
There are others. I find these small tube types fascinating. Imagine a whole functioning tube amp that would fit into a tube screamer pedal.
1 watt is still plenty loud. You could make a 1/4 watt amp that still makes plenty sound. If you designed it for headphones only you could reduce power output even more. REmember those little solid state amps built into cigarette packs?