Considering it's a 1967 model in GT3, based on an even older car with a 7 litre V8 shoved in, I'd guess at a 4-speed.
However, I don't believe for a second that it tops out at 137mph, like in GT3. A Cobra allegedly reached 165mph on the M1 in England in 1969 - leading indirectly to a national speed limit of 70mph being enforced...