Just warning you, it's the most tedious, life-endingly boring task you could possibly imagine. I like to imagine that they had people wind Tesla Coils as punishment during the Inquisition.
Two days and you'll have a high-impedance transformer in your hands.
If not, buy an electric drill, get a bobbin, or a piece of cardboard with tape face-up on it, and enjoy the next day or so.
And yes, a resistor is not going to act like an inductor, but to the primary it will look like it if you put it on the secondary in line with your load, because you are essentially floating the other side independent of the primary. The current is proportional to the load and turn ratio, if you have the same ratio of turns, it's proportional to the load, just like anything.
On top of that, a resistor is unchanging with frequencies of our level, so it's wayyyy better.
It's the same reason you can turn a MOSFET on carrying 10,000 volts with a 15V floating signal. The reference is not 0, it's V. The reference for your primary's current output is not the primary itself, it's whatever is on the secondary.
A well done 10000R impedance coil is hell to wind, especially if you aren't operating at a high enough frequency to warrant it, but it's doable.
For example's sake, I have a 200~ turn coil at 100kHz and got
$$ X_L = 2 \pi (100000)(0.025) $$
$$ X_L = 15000 $$
At your frequency, with my coil, you only get
$$ X_L = 2 \pi (20000)(0.025) $$
$$ X_L = 3141 $$
And that's your maximum.
So you'd have to wind three of mine, just about. So 600~ turns of 28(?) gauge copper wire for a radius of 25cm and a center hole of 5cm radius.
It's really kind of horrible to wind that much.