Technical science is a roll up of the "dry sciences" (physics, engineering) but abstracted at higher tech level than your every day things. This is to say that the Technical Science skill alone cannot substitute for the Handyman skill. Typically, Technical Science challenges will require a broad range of specialized tools, that will usually be combined into an abstract "Workshop". If a location is designated a Workshop please consider that it meets the prerequisites for any Technical Science challenges requiring such, even if the specific tools you may need are not represented by props. As a skill, we expect Technical Science to have a great deal of effect on the campaign-wide plot. In addition, Technical Science can be used to repair broken Greentec items, and is also a requirement (in addition to Handyman) to perform Weapon Repair - Firearm.
In any given game, there may be challenges specific to that scenario. The details of that challenge will be available on the site of the challenge. Some of these may be multi-layered challenges, and those details will also be contained therein.