You asked if it's possible, or some alternative; yes, it is absolutely possible, so no alternative is needed. You hadn't indicated what else you're lacking, so...
The type of the Sziklai pair is defined by the input transistor, yes. The input transistor only needs to be rated for the base current required by the output transistor, and both need to be rated for operating voltage and power dissipation. Some typical caveats include potential for oscillation, and proper design of current limiting or other protective means.
Oscillation can happen for a combination of reasons: the input transistor is typically rated for less current and more fT, while the output transistor has a lower fT, longer lead lengths and higher capacitances; this introduces more gain and phase shift in the C-E path of the input transistor, which can push the combination into oscillation. Whereas a Darlington has Miller effect (C-B feedback) and emitter degeneration (the one emitter is cascaded into the next base).
Note that an emitter resistor on the output transistor essentially accomplishes nothing. If an emitter resistor is used for degeneration or limiting, it goes on the composite/equivalent emitter terminal. Which is obvious when drawn with the equivalent/composite, but it's been missed before...
Tim