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I wouldn't have any real concerns about clamping down (relatively) soft wood to allow planing.
I don't know if Keter actually manufacture those clamps.
Irwin, who do manufacture a range of clamps do supply different clamping force,
cheapest, force unspecified, (150/300mm length)
medium duty, 136kg, (150-900mm)
heavy duty, 272kg, (150-900mm).
If you had a real c0ncern Toolstation stock the Irwin medium duty, (heavy are 'next day').You could relieve some of the stress on both the planer and the clamps by cutting a series of shallow cuts with a saw, (hand/powered), to remove most of the unwanted timber.
@aggi or @mespilus re the workmate alternatives are the jaws and overall structure sufficient to plan wood?
In my case a c.30cm long peice of wood.
@jono84 what did you go with in the end? Sadly my dad's workmate now seems at the end of its life as I can't grip wood to plane. And unfortunately the cost of replacing the top makes repairing prohibitively expensive.