Discuss whether a change in controller medication or decrease in the dose or strength of the inhalant would be an option. Some health experts have reported a reduction in hoarseness after backing down the dose, but this is not always effective. There is a particular inhaled steroid which is inactive until it reaches the surface of the lung (after inhalation). It seems to be an ideal inhalant for people who have adverse effects which are localized to the throat or tongue. The brand name of this unique inhaled steroid is Alvesco. It is only available by prescription. Unfortunately no currently available steroid based inhaler, (including Alvesco) eliminates the risk of dysphonia. One study referenced below suggested reduced risk with some dry powder inhalers.
Corticosteroids have been used as drug treatment for some time. Lewis Sarett of Merck & Co. was the first to synthesize cortisone, using a complicated 36-step process that started with deoxycholic acid, which was extracted from ox bile .  The low efficiency of converting deoxycholic acid into cortisone led to a cost of US $200 per gram. Russell Marker , at Syntex , discovered a much cheaper and more convenient starting material, diosgenin from wild Mexican yams . His conversion of diosgenin into progesterone by a four-step process now known as Marker degradation was an important step in mass production of all steroidal hormones, including cortisone and chemicals used in hormonal contraception .  In 1952, . Peterson and . Murray of Upjohn developed a process that used Rhizopus mold to oxidize progesterone into a compound that was readily converted to cortisone.  The ability to cheaply synthesize large quantities of cortisone from the diosgenin in yams resulted in a rapid drop in price to US $6 per gram, falling to $ per gram by 1980. Percy Julian's research also aided progress in the field.  The exact nature of cortisone's anti-inflammatory action remained a mystery for years after, however, until the leukocyte adhesion cascade and the role of phospholipase A2 in the production of prostaglandins and leukotrienes was fully understood in the early 1980s.
Early on when taking these drugs (hormones), you can simplistically think of the medication as "supplementing" your body's own production of corticosteroids. With time, your body realizes you are getting all of the corticosteroids you need in pill or intravenous form, and your body sends a message to stop producing your own natural corticosteroids. If these drugs are suddenly stopped, you not only are not getting the prescription, but it can take a significant amount of time before your body realizes that it needs to make its own corticosteroids again.