It isn't clear from that picture, but the Marshall MS-2 Mini Amp (Musiciansfriend.com Product #482812) is $34.99 and 5.75 inches (14.6cm) tall, about 4 inches/10cm wide. This image is just about life-size:
I have calculators bigger than that!
I don't think it is impossible to put a tube in there... but even just a 12AX7 with speaker transformer and power supply will fill the cute case, and probably melt it.
And from the reviews, it is a damm-fine pocket-amp the way it is.
And its key shortcoming may be its diminutive size, its acoustic projection and balls. You can't change the fact that it is a 3" speaker in a 4" box. A gitar amp should be at least as big as an acoustic guitar body, to be impressive.
I'd have to dig through the boring pages of the tube manual to pick a low-watt 7-pin output tube. You could fit that plus a speaker transformer, but the case would get soft from the heat, and the power supply has to be external (or hot-chassis, but I love you too much to allow that). Adding a preamp tube to bring pickup level to power-tube level would be a real tight fit, and probably make the case sag from heat.
You could keep the existing power-amp, there can't be much wrong with it, and add a hearing-aid tube as the preamp. Still needs external power, though it could be a C-cell and five 9V batts.
As a Very Advanced Project, you could maybe develop a push-pull parallel quad-array of hearing-aid tubes to make nearly the same audio power without an impossible amount of heat. Plus three more tubes for preamp, driver, phase-splitter.
Or were you thinking of putting the tubes on top? That would reduce the heat issues.
I still think the joke isn't worth the effort.