Cooldown text is one of the regions of cooldown frame, currently it's the first one, so I "hide" it this way:
Lua Code:
local text = CooldownFrame:GetRegions()
text:SetAlpha(0)
You may try to force hide it, doing something like this to regions normally doesn't cause problems, but I dun remember whether it's a taint-free solution or not. But there's definitely an issue, cuz I dun use it in this case, hehe...
Lua Code:
local text = CooldownFrame:GetRegions()
text:Hide()
text.Show = text.Hide
You may try to re-parent it to a hidden dummy frame.