/replaceitem entity @p slot.armor.head minecraft:-ITEMNAME-

...and...

/give @p minecraft:-ITEMNAME-

...do not give the player anything/put anything on their head.

replace -ITEMNAME- with:

fire
portal
(possibly more, haven't tested)

additionally, the missing textures is shown on the players head if you try do do any block with a damage value other than 0, such as a trapdoor with a damage value of 12.