Think carefully about using the standardized mean difference, as it confounds the objective effects of the intervention with the design of the study. Heterogeneity is always a critical factor in the conclusions you can draw from retrospective meta-analyses.
If your measurement has a natural unit, it is generally agreed that this is a valid way to aggregate different studies.
You would not know this from the easily accessible literature on how to do a meta-analysis. I’ve collected a lot of papers in a separate thread, but the most important ones are described here: