Ordinary transformers tend not to be pulse rated, so you would need to do your own calculations of copper mass and temperature rise. Fortunately it's quite easy to do your own measurements of temperature rise. Copper resistance increases by 0.4% per degree, or 10% for 25 C, so you make a measurement of winding resistance, apply a short high current pulse, and re-measure the resistance quickly, before the winding heat dissipates into the core. The maximum permissible rise is governed by the temperature handling of the insulation, which may or may not be specified by the supplier. Don't forget that this adiabatic rise happens on top of the starting temperature of the transformer. You do not need to measure lots of different pulse lengths to characterise as, once in the adiabatic region, the I2t stays constant.
The transformer still needs a continuous rating to handle the average load, so how many one second pulses are you going to deliver per minute? If you deliver six per minute, that's a 10% duty cycle, and a 200 VA transformer ought to be able to handle the average dissipation.
Transformers are often rated somewhere around 5% regulation. Using a transformer at 10x its rated continuous current would probably give you 50% regulation, still adequate for your testing purposes. This figure means you should not go much smaller than 200 VA without proper calculationsIt would also give 100x the dissipation, so take that into account when calculating the duty cycle and average dissipation.
Finally, to your actual question, whether to use toroidal or a conventional lamination stack?
FWIW, I had to source one 6 V 100 A continuously rated transformer, for testing smart meters. Nothing with that winding ratio was available off the shelf, and I was quoted silly money to have one made. So I bought the cheapest 600 VA toroidal transformer that I could from a catalogue, and stripped the secondary winding from it to make more room, leaving the earthed screen and the primary underneath it intact. I then wound a new secondary with a few turns of 32 mm2 (actually bifilar 16 mm2!) plastic insulated single core cable. A toroidal was ideal in that case as thea short secondary can simply be passedthreaded through the hole.
It might be nice to be able to select the ratio of the transformer, so you don't need as much flexibility in how you drive it. A favourite technique of mine, to minimise the number of connections and so extra space and secondary resistance, is to use a tapped secondary, and to manually connect to the required taps. For instance, if you use 6 turns, tapped at 0, 1, 4, and 6 turns, you can pick off 1, 2, 3, 4, 5, and 6 turns, using onlyby taking output from the appropriate two connections (you would have to use two anyway). This is incidentally the minimum arrangement for 4 taps, each possible connection gives a different number of turns. You can extend the principle by adding a further 3 turn windingswinding or two in the middle to give up to 9 turns with 5 taps (nice for a decimal box) andor up to 12 turns with 6 taps. It gets a bit unwieldy after that, and a binary setup starts to look more attractive.