Reach to brakes and drops depends on the throw (distance forwards from the straight part of the bar) and drop of the bars, so the reach of the 38s will depend on whether they have a shorter throw and shallower drop than your current bars.
If your physio is suggesting 40s, he/she must think the 42s are too wide, which usually means they splay your arms out wide (rather than straight ahead). In that case, a narrower bar would help a little because your arms would be forward rather than forward and out to the side but 38s may well be too narrow and leave you feeling cramped. (Some measure differently though, so I'd measure.) Drop and throw varies quite a lot with different models; you can sometimes find it on the manufacturer's website. Note that a short throw/drop bar like the FSA wing pro compact is also wider at the bar ends than on top, which may or may not suit if you are looking at options.
Changing bars is more hassle and cost (changing hoods and bar tape) than switching to a shorter stem but still worthwhile doing for fit and handling. But I'd look at stem length as well.



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