I've done a lot of time in Aztrucks and can assure you that they go nowhere but down on one engine, with gear and flap extended. Its not just a matter of getting rid of the flap either. In the classic flight check scenario of engine failure after take-off, with no usable runway left, always get the gear away and consider my flap options.
I say "consider my flap options" because the Aztruck I have most time on was fitted with a Robertson STOL conversion, so the flaps were flaperons. In a standard machine, I'd get rid of the flaps without a second thought.
With the engine failure on approach in the Aztec, I'm going to land, not go around. And, if I have to use the hand pump, so be it. Planning for this will modify the way I manoeuvre to get back to the runway, but I wouldn't be too concerned about using flap during the approach unless I was especially high - and I'd try to avoid that scenario too, if I was you.
I always brief myself on what I'll do in the event of engine failure before, during or after take-off. As part of my forward planning for a landing, I'll brief myself, about 30 miles out, about engine failure during the approach and landing. Then I plan to stick to that plan because it takes account of known weather conditions and as much info as I have on other aircraft in the area.