Think the DSO and DUT rise times are independent and should follow as:
Measurement RT^2 = DSO_RT^2 + DUT_RT^2, or Measurement RT = Square Root (DSO_RT^2 + DUT_RT^2)
1st order model for DSO RT is ~ 0.35/BW where BW is DSO -3dB Bandwidth. Since this is Root-Sum-Squared measurement (common in many effects) the usual ~5X Tektronix recommended better scope rise time only causes ~2% measurement effect.
So one could get a pretty good estimate of the actual DUT rise time with different DSOs with different BWs following the above guide lines.
Best,
Edit added for those interested:
The 1st order DSO scope model assumes a single pole response, higher order responses are expected in higher BW DSOs which involve a more complex frequency response than a single pole.
If you assume a single pole response then the DSO BW follows:
1/(1+(w/wc)^2) = 1/2, where wc is the DSO "corner" half power or -3dB frequency in radians/s, or 2*pi*BW where BW is in Hz.
The single pole DSO time step response will follow:
Step Response = 1-exp^(t/tau), where tau is the DSO time constant which equals 1/wc.
So the 10% step response is 0.1 = 1-exp^(t1/tau) and the 90% step response is 0.9 = 1-exp^(t2/tau), or
t1 = -tau(ln(0.9)) and t2 = -tau(ln(0.1)
10% to 90% rise time = t2-t1, or tau( ln(0.9) -ln(0.1)), or tau ln(9),
then 10-90% rise time = ln(9)/wc, or ln(9)/2*pi*BW, or 0.3497/BW