I hope you are planning on re-siliconing the spot where it was leaking. Just removing that 4mm gap alone will not fix it. If it was leaking that means there IS a break in the silicon, and you WILL have to repair that. Fixing the stand gap will prevent it from happening again.
I would go with plywood idea. If you use 1" plywood it won't move much even under the tremendous weight of a tank, and you won't have to rely on the chintsy shims as much as if you use thinner ply. You can buy a small piece of thin trim (so it's bendable), glue that on the viewable edge of the plywood, and stain it to match.
PS I'm a renovation carpenter, so my advice comes from building experience.
