It’s a little more complicated than just knowing the chemical makeup of a transistor. Transistors aren’t made just by combining chemicals. Transistors are “grown”. You basically start with a puddle of molten silicon. It can’t have too many impurities in it (don’t ask me if this is possible in 1905). Now, you basically “grow” a silicon crystal out of it, but here’s the catch. You have to add certain types of impurities while the crystal is growing.
Transistors are made out of N and P type silicon. If your silicon crystals contain some bits of phosphorus, arsenic, or antimony (hint - these are all in the same column on the periodic table) you end up with N type silicon. If your impurities are boron, aluminum, gallium, or indium (again, all from the same column in the periodic table) you end up with P type silicon. A layer of N type silicon grown on top of a layer of P type silicon makes a diode. NPN or PNP makes a transistor.
I don’t know what was available in 1905, but just examining a modern transistor using spectral analysis and looking at it under a microscope is just going to baffle someone from 1905. If you can explain the basic physical and chemical properties, maybe you’ve got a shot at it, but if someone without any knowledge of semiconductors takes one back with them, the chances of a 1905 scientist being able to reverse engineer the thing probably aren’t good.