Try to measure it as is, soldered into circuit. You may get distorted value, but better than nothing, if it disintegrates during removal.
Then, I'd cut the longer lead, to remove it from circuit from one side and measure it again - this should yield accurate value, but at risk of damaging the resistor. Use thin cutter, to avoid bending of the leads/resistor as much as possible.
Also, try to find out why the resistor was so much damaged. The new one will get as hot as this old. Maybe it's designed to run as hot, maybe something is wrong with the PSU - perhaps leaky capacitors?