Using 32P is not particularly dangerous - if you have the appropriate training, work carefully and the lab and work space are organized appropriately. However, and alternative approach is to use non-radioactive ATP in an in vitro kinase assay and then probe with an appropriate anti phospho antibody. For example, there are anti phosphorylated tyrosine antibodies. If you are interested in a particular substrate, you may be able to use anti phospho antibodies to specific sites in your protein of interest. A drawback to assessing phosphorylation by immunoblotting is the narrow dynamic range when using film. This can be overcome using acquisition systems to directly capture the signal. Such systems generally have a dynamic range extending over several orders of magnitude. Systems are available for either ECL or fluorescence.
A replacement for 32P is 33P. It has a less energetic beta decay and is therefore safer to work with. It also has a longer half-life than 32P. You should still be sure to use appropriate safety measures.