First of all, you can tell HyperSizer to perform strength and local buckling analyses for "peak" loads by choosing "Element Based" from the FEA Statistical Loading Method selection on the Design-To Loads tab of the sizing form. This will tell HyperSizer to do an analysis for every element and return the lowest margin of safety for any element and therefore capturing the "peak" load.

For Beam Buckling, that is, buckling of the entire beam as with Euler column buckling, HyperSizer will use the average compressive load, regardless of the selection of statistical loading method. This still seems to be appropriate as this type of failure mode, column buckling, would not be susceptible to load peaks but rather is an average effect for load in the overall column.

For more localized buckling effects, such as buckling of the web of a beam, or for circular tube beams, cylindrical buckling of the wall, these are considered local buckling effects and would actually use the same loads as those used for strength. So if you turned on element based, then the local buckling analyses will be done element by element.

Are these the kind of buckling effects that you are considering when you talk about beam buckling?

As of now, there is no way to tell HyperSizer to use peak element loads for the overall column buckling.