Converting a cis-alkene to trans-alkene
Your method looks fine. There is another simple method (with three steps though).

Convert the the cis alkene to a dibromo derivative using bromine;
Use two equivalents of $\ce{NaNH2}$ to get an alkyne (elimination);
Selective reduction to trans alkene by using sodium in liquid ammonia.
However this requires that Hydrogen be present as a substituent on the double bond, on both carbons.