At first I thought I'd look at underwater x-ray (minimal disturbance to the carcass), and it turns out the only people interested in this is the navy! Not for carcasses, but for examining sonar domes on ships without having to dry-dock (Greenawald et al., 1998). So it seems unlikely that this is a feasible option.
Greenawald, E. C., Poranski Jnr, C. F., Levenberry, L. J., Bellinger Jnr., E. T., 1998. Underwater x-ray tomography of composite sonar domes via collimated backscatter imaging. Proc. SPIE 3396, 121. http://dx.doi.org/10.1117/12.30151
Richter, A., Wuttke, M., 2012. Analysing the taphonomy of Mesozoic lizard aggregates from Uña (eastern Spain) by X-ray controlled decay experiments. Palaeobiodiversity and Palaeoenvironments, published online. http://dx.doi.org/10.1007/s12549-011-0065-1