The choice between LC-MS or GC-MS depend fo the characteristics of your pesticide.

The determination of the chromatography method depends on the pesticide (solubility versus volatility), expected concentration (ppt), and the challenge of the sample matrix (the insect body).

Spectrophotometry?

There are several options besides LC-MS and GC-MS. Raman spectroscopy could be useful, as well as mass spectrometry with ionization techniques like MALDI, DESI, SIMS.

The best approach that will likely capture the largest number of pesticides is HPLC-MS/MS. Every manufacturer has an application note for this type of analysis. Here is one from Agilent looking at 250 different pesticides in a single run.

https://www.agilent.com/cs/library/applications/5991-6357EN.pdf

I'm sure you could find something very similar from Sciex, Waters or Thermo as well.

You should also consider if you are willing to destroy your sample (e.g. for a liquid/liquid or liquid/solid extraction), how much of the samples you have. Did your specimens die from an acute intoxication or are you just curious about the potential exposure they had? For a better picture you would need both GC/MS and LC/MS. For instance, neonicotinoid pesticides are typically analyzed by LC/MS whereas pyrethroids are easier to analyze via GC/MS; organophosphate pesticides have a wide range of polarity and you are likely to require both analytical platforms, the same happens for different families of anti fungal agents (yes, their analysis for insects is important too), while carbamate pesticides are better handled with LC/MS.

insects: for example bees, take care of the extraction technique, LC-MS/MS best choice, depend on chemical family (pesticides).

Thanks for all the answers.