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Too late now!
I picked up a ERBAUER ERO400 125MM ELECTRIC RANDOM ORBITAL SANDER
Got to say I'm quite impressed and wish I'd got one earlier. Managed to sand the biggest bit of the drawers outside, but then had to do the rest of it in the kitchen.
Obviously it's hard to know how much other dust but with the hoover attached I was pretty impressed at how well it worked.
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I found my hoover (a Miele one with replaceable bags and filters)
a) didn't capture all the dust in the filters so each time I turned the hoover on for a while it blew out a plume of fine dust;
b) got clogged up with all the fine dust and overheated and kept shutting down until I took it outside and brushed all the dust off.
Forgot to mention in previous replies it's a rotary sander not random orbital that I would prefer in this case. RO might work as well but having the choice I usually opt for rotary.