How to identify what type of filament an unlabeled spool is
Mick's suggestion is a good one. PLA may shed some color in acetone, but ABS will dissolve completely in a suitable amount of time. If you have dark filament, you can test by flexing the filament until it breaks. ABS will sometimes/often/usually fatigue with a white break line, while PLA does not exhibit this tendency as much.
PLA has a somewhat sweet smell, which may be the corn sugars burning off, while ABS has a much more chemical-like odor.
Not doing heat testing does limit your options.