medication that does not cause tremors

I hear you.  I take Advair (similar to Symbicort) and Ventolin as needed and have a slight tremor as a result.  Even though part of my job is drawing blood, I've managed to work around this pretty well thus far.  If there was a asthma medicine that didn't have the tremor side effect I'd be the first one to try it. 

You just have to decide what's more important:  a steady hand or breathing well.  I've decided I like to breath more, as I'm sure you will too. 

That said, if you're having the side effects you're describing above from Symbicort you are best to discuss this with your physician as he may want to find an alternative medicine for you to try.