Mineral oil will not absorb into skin or hair, it's far too large a molecule and totally unnatural so your skin would not know what to do with it anyway. Since mineral oil is inert I assume it's there simply as a barrier, to stop the skin or the active ingredients drying out or being rubbed off.
Neutrogena T-Sal shampoo is sulphate free and contains salicylic acid. Sulphate free shampoo containing cocoamidopropyl betaine should also work fine to shift mineral oil. Probably not a wise move to use anything containing other oils or moisturising ingredients, just something plain like a pH 4.5 to 5.5 shampoo 'base'. Ideally you need the salicylic acid, that is the keratolytic that loosens the psoriasis plaques so they can lift off.
Have you tried scalp only washes? Wet the head and hair, coat the lengths in conditioner as protection if you are permitted to use it, use a nozzle bottle to apply the slightly diluted shampoo to your scalp only. Thereafter wash and rinse as normal.
Spray gel and mousse might not be the best idea, you will struggle not to hit your scalp with that, and they tend to be packed with potential irritants. You might find aloe vera inner leaf gel, DIY okra gel/ flaxseed gel or a combination gentle enough, have you ever tried any of them as stylers?
Once your psoriasis is back under control you might speak to Komaza Care about what products of theirs would suit you, they are very into scalp health and use some really beneficial ingredients..