Which one to state — "We would like to thank You" or "We thank You"

"Would like to" is often a buffer, implying either tentativeness or extreme politeness.

In speech "I would like to thank" is much more common than "I thank", because these formulas are pretty well confined to formal settings, where extreme politeness is preferred.

In a commemorative plaque, either is possible, but I would go for the shorter form.

Incidentally, it is not common to capitalise "you".

How about just "Thank you for your unstinting support..."?

"We would like to thank you" is a common way of phrasing it, but perhaps a bit conversational for an official plaque.

"We thank you" is less common, but still acceptible. To me, it the "We" stands out due to this phrasing's relative rarity in comparison with the simpler "Thank you", putting the emphasis on the fact that it is a collective act of thanks. This possibly explains the popularity of this phrasing in prayers.

I would think that the speech presenting the plaques would involve the line;

We would like to thank you for your service by presenting you with these plaques.

The plaques themselves would simply say

In recognition of so and so you have our thanks.

When I read/hear "we would like to ..." I think: please go right ahead! I'm waiting!

"We would like to ..." seems to be yet another phrase we use to avoid getting to the point.

Please just say, "Thank you for ..."

That's the best way.