First approach is definitely WRONG. Take a look at the paper "Inappropriate Use of Bivariable Analysis to Screen Risk Factors for Use in Multivariable Analysis", J Clin Epidemiol Vol. 49, No. 8, pp. 907-916, 1996.

Regarding the second approach, you should include ALL relevant variables: known risk factors of death in kidney transplanted patients, age & gender as usual suspects, other potential confounders, effect modifiers ("is the effect of NODAT on survival modified by other factors?")... If any of them violate the PH assumption, there are statistical methods to control that (stratification, time-dependent covariate Cox model...), but an important predictor should not be left out of the model just because the PH assumption is not met.

• "To Explain or to Predict?", Statistical Science 2010, Vol. 25, No. 3, 289–310
• Mitchell Katz "Multivariable Analysis: A Primer for Readers of Medical Research", Ann Intern Med. 2003;138:644-650.
  

Marta GG