Seems you can buy refillable inhalers. You soak the cotton wick in essential oils of your choice, put in the inhaler and sniff away.
If you live in the States you can buy these rather nice ones in glass and aluminium from Amazon.com 3.5 inches x .75 inches, outer shell is aluminum.
If you live in the U.K. you have to make do with these ugly plastic ones from Ebay. Yes, I know, plastic – but reusable rather than disposable.
Find more #plasticfree personal care products here