TLC could work - you will be able to detect low concentrations of styrene with a permanganate stain. You'll have to compare the GC with TLC a few times to see what <0.1% looks like on TLC, and to see what complete consumption by TLC looks like by GC. You also need to standardise the concentration and volume of the TLC spot.
The limit of detection might be higher than 0.1% for TLC, but I reckon styrene + permanganate has a chance.