How many days per ref in TF2?

Bare minimum? Given 1 Refined == 9 Scrap at 2 weapons apiece, 18 play sessions of ~45-50mins.

A drop can happen anywhere between 30 and 70 minutes (with 50 minutes being the average), so you may have to vary your play times a bit if you want to guarantee a drop.

Of course, all this is assuming that each drop is a compatible class weapon to be used in smelting. Remember, in order to scrap two weapons, they must come from the same class. For example,

• You can scrap a Sandvich with a Tomislav (both for Heavy)
• You can scrap a Force-a-Nature with a Mad Milk (both for Scout)
• You can't scrap a Sandvich (Heavy) with a Mad Milk (Scout)

So realistically it will probably take a bit longer than 18 sessions.

You could also swap/trade for compatible weapons to make the process quicker. Sites like Scrap.TF make this easier. Of course, once you go down that route it may just be easier to trade for what you want rather than worrying about scrapping & crafting stuff.

You can read more about Drops and Crafting on the TF2 Wiki.