8-speed freewheels are rare and not made by Shimano or Campy since the unsupported length of axle on the drive side is worst than 6 or 7-speeds and makes them even more breakage prone.

That said, you will have to respace the hub to 130 mm to get an 8-speed freewheel to fit properly. This can be done with your 126 mm hub by adding 4 mm of spacers to the drive side to move the locknut out far enough to let the small cog clear the chainstay and dropout. You may be lucky enough not to need all 4 mm on the drive side so add the extra, if any, to the non-drive side which will reduce the needed dish.

You can probably retain your current 137 mm long axle. The protrusion past each locknut will be reduced from the standard 5.5 mm per side to 3.5 mm per side but that is adequate.