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If the emphasis is on cheap, there are a few things you might already have at home:
Possibly acetone - try cheap nail varnish remover
Possibly isopropyl alcohol - try surgical spirits / rubbing alcohol
Possibly methylene chloride - try paint stripper but be aware of the fumesI've used nail varnish remover in the past to remove excess thread locking compound during assembly - not sure how different it is when it's had time to cure...
Alternative, cheap, solvent to official one for blue Loctite? So far a little googling says acetone.