Scope voltage drop across a 7R5 resistor
Calibrating the gain on each channel is critical for differential mode (DM) with this very low DM/CM ratio. 7mV/3.7V * 100%= 0.19%.  You cannot do this by eye on the scope so a DSO calibration is key and may not be easy to adjust.

For resolution this and power dissipation reasons, a 1% max Vdrop is computed for current sense R or 75mV is often standard.  This raises your load regulation error by 1% which is tolerable.

Thus I would suggest a 75 Ohm R and expect a 53mV drop with 700uA drain.