Using seat-of-the-pants observations, the product of size and weight versus output power should be a pretty clear indicator f linear vs. switching. Also, you can measure the unloaded output voltage. The vast majority of linear wall warts are unregulated, and 50% overvoltage unloaded is possible. OTOH, the vast majority of switching ww's are at least loosely regulated within 5% or 10%.
Separate from that, what is the system and why does it require a linear ww? That might be mystical thinking on the part of the original designer, someone who had a bad experience with a switching ww but didn't/couldn't figure out why.
ak