Yes it is odd and we wouldn't say it. If someone says 'make a wish' (on someone's birthday when they blow out the candles on the cake for example) then it is implicit that the wish is not to be vocalised. The reason being that there is a superstition that if you say the wish out loud it will not come true.

Damn typo. *When would you use it?

I can honestly I have never heard anyone say that sentence. When you would use it? It sounds highly strange to me.

*I can honestly say...

@ Paul. There is a meaning to saying "make a silent wish". I couldn't work out your first sentence. If you hadn't written "Yes it is odd and we wouldn't say it", I would have been less confused by your answer.