Is it possible to compute delay with an IIR filter between peaks?
It is possible with an IIR filter, but not accurately with a plain Butterworth filter. As far as I can recall, the only IIR filter with flat group delay is the Bessel, whose stopband attenuation is inferior to the Butterworth.

The problem with the Butterworth is that the group delay is a function of frequency, therefore the different frequency components of your peaks are delayed by different times.

One solution is to follow the Butterworth filter with a "group delay equaliser" consisting of approximately as many "all pass" stages as the filter itself. This will give you a good approximation to a constant group delay. I wouldn't presume to advise you on actually designing the equaliser.

All in all, I think the FIR filter is a far simpler approach, as well as more accurate : I don't know why you regard its delay as "approximate".