Determine characteristics of unknown choke
There is a way to find out by using just one of the two coils. Use a wide-band sine-wave generator and the scope to read/catch the -6 dB roll-off point. This is an inductor-not a resistor, so it has a -6 dB at the roll-off point.

First test the DC resistance of both coils to make sure it is a CM choke and not a transformer. Both coils should have exactly the same resistance.

You have \$L\$ which is unknown, so you add a known value of \$C\$ (100nF poly)to form a common LC filter. Measure across the capacitor with the choke winding in series with your signal generator. Now as you sweep upward in frequency there maybe a slight peak before the -6 dB drop, which will continue to drop. At that -6 dB point is the resonate frequency using the capacitor.Use 

$$L = \frac{1}{4\pi^2\cdot F^2\cdot C}$$

where \$F\$ (in Hz) is the -6 dB point and \$C\$ is the capacitance (in Farads) used. \$L\$ is in Henries.

\$2π \cdot F \cdot L\$ gives you the \$X_L\$, or inductive reactance in ohms. \$X_L/R\$ with \$R\$ being the DC resistance of one coil gives you the \$Q\$, or efficiency of the inductor/choke. This may change as you change capacitors. My guess is the choke is 300 uH to 3 mH, with a high \$Q\$ rating if wound with heavy gauge wire.

Now you have the value of \$L\$ and \$F\$. Measuring the inductance with no capacitor is tricky, as it depends on local stray capacitance to set up a resonate point. I suggest you try many values of \$C\$, which will change the -6dB point, so that higher and lower intensity peaks are found based on the same equation.

A spectrum analyser would be nice but...