The reason manufacturers don't always publish that info is precisely because those cameras are so slow. If the model is faster than average for that class of camera, you can be assured the manufacturer will tout that ability to no end!

The best way I have found is to do an internet search that includes the camera's model number and the words "shutter lag". You will usually find at least a review or two that mentions the camera's performance in this regard.

A google search for Olympus SZ-31MR shutter lag (that was the camera in the dp review link in your question) led me to the following review which included a comparison between that model and several other cameras in the same market niche. Although each site's methodology may vary and you can't necessarily compare the 'shutter lag' measured for one camera by c-net to the "shutter lag' of another model measured by another review site, you can compare the relative performances of different cameras tested by the same reviewer.