I did a quick Google search and I see that the Shindo Apetite has no tape or other line-level output; it has only one set of output terminals per channel, rather than multiple taps; it is rated at 15 watts into 8 ohms; and it certainly has an output transformer since its output stage consists of a push-pull pair of 6V6 tubes per channel.
If the headphones are low impedance, for example 32 ohms, then as Czarivey pointed out driving them directly from the amplifier outputs would risk blowing up the headphones and/or your ears if the volume control is not kept very close to the bottom of its range.
If the headphones are high impedance, for example 300 ohms or more, that would be less of a problem but you would risk damaging the amplifier if you simply connected the phones directly to it. A tube amp having an output transformer should never be operated without a speaker or equivalent load being connected, or the output transformer and/or the output tubes may be damaged due to what is called "inductive kickback." I would expect that a load that is measured in hundreds of ohms, and perhaps even less, would be high enough to make that risk a real possibility.
One possible approach would be to get a pair of high impedance phones, such as
this 600 ohm model from Beyerdynamic, or one of several other high impedance models they offer, and connect it to the amplifier outputs in parallel with an 8 ohm high power resistor, rated to handle say 20 or 25 watts or thereabouts and preferably a non-inductive type, one resistor for each channel.
That should work, although I suspect that you would still have to be careful with the volume control setting.
Alternatively, if you can find a suitable matching transformer, that would step down the amplifier's output voltage enough to be in a good area relative to the impedance and sensitivity of the phones, you could use that together with a similar 8 ohm high power resistor connected across the primary of the transformer (or, equivalently, connected across the output terminals of the amplifier), for each channel. (Without the resistor a step-down transformer between the amplifier outputs and the headphones would cause the amplifier to see an even higher impedance than if the headphones were connected directly to it, causing an even greater risk of inductive kickback damage).
A third possible approach would be to connect a high power resistor that is a little higher than 8 ohms across each channel, and in parallel with it connect 2 additional resistors that are in series with each other. The signal to the phones would be taken across one of those two resistors, whose values would be chosen to divide down the amplifier's output voltage by an amount that would be calculated based on the impedance and sensitivity of the particular phones. For several reasons it would be preferable to use that approach with phones having medium or high impedance, and avoid using phones having low impedance.
Regards,
-- Al
