Can a government or central bank work to reduce inflation without hiking interest rates and causing the currency to appreciate? Since trying to lower inflation will have some undesirable consequences, such as currency appreciation, which hurts exports, should governments and central banks keep hands off on inflation? 
But exports would become uncompetitive anyway when inflation is high (as prices increase).
In a high inflation scenario, what should government or central bank do to protect exports (in an export dependent economy)?
Yes, but only if you also introduce capital controls. You should check out the Mundell–Fleming trilemma:


  The Impossible trinity (also known as the Trilemma) is a trilemma in
  international economics which states that it is impossible to have all
  three of the following at the same time:
  
  
  A fixed foreign exchange rate
  Free capital movement (absence of capital controls)
  An independent monetary policy
  


Wikipedia Impossible Trinity