Cruise makes no difference.
Basically, unless the 182 box has a speedo drive, you'll lose the speedo reading.
Ph1 172's and 172 Cups (and some very early Ph2 172 parts bin specials) use the speedo sensors on the back of the gearbox to give the speedo reading. Ph2 172's and 182's use the ABS sensors.
Meaning you can fit a Ph1/Cup box to a 172/182 with no issues, but the other way round and the speedo will stop.