Just don't tell them why you want one. Nothing more suspiscious than entering into a long tale of why you want to purchase something potentially dodgy.
BTW medicine (oral)syringes etc don't have the right type of fitting for needles, so a chemist is unlikely to raise an eyebrow at selling you one unless you look particularly dodgy.
The tip re child nurofen is useful, I'd forgotten that they had those little 5 ml tube type syringes included.
Whatever you end up with, clean it out thoroughly after use as the lubes & oils we use in suspension forks don't agree with the rubber used on the end of the syringe plungers & will cause the rubber to swell & jam in the syringe barrel.