Unneeded hole in the wooden partition or details it is easy to putty. However, such a tube may eventually shrink or crack and fall out.
This does not happen, if before applying the putty into the hole to fill the nails: they will play a role of reinforcement and sealing holes will be more reliable and durable.
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If you don't have the rivets you need sizes, don't rush to the store. Better fabricate a device which you can use to make rivets of all sizes. Tools required the simplest set of drill...