Wafer -- New Adjective or Attributive Noun?

This is not a particularly new use in discussing British government.

The 1970 book The battle of Downing Street says:

The wafer majority of his Government...

The 1976 book Walking on the water says:

When the dust had settled, leaving Harold Wilson with his wafer majority of five

The 1984 Pricing, Planning and Politics refers to:

a wafer majority of four parliamentary seats

But even earlier (1950) there is the term "wafer margin" in Best Sports Stories (reprinting the story "Homer by Henrich" Worcester Telegram 5 October 1949):

provided Allie Reynolds the wafer margin by which he bested Don Newcombe while 66,224 spectators sat on the edges of their seats in Yankee Stadium

(referring to the 1-0 win of the Yankees over the Dodgers in the 1st game of the 1949 World Series, due to Henrich's bottom of the 9th walk-off home run)

So, like these examples, in the OP "wafer" is an adjective and means "small" or "thin".