One of Richard's points about anglicisms may have been that English borrowings often take on an altered meaning in German (Handy, Bodybag, etc.). Barring further proof for the *English* side, I'm not convinced that the word 'strip' is really used alone in this sense. As far as I know, real people don't say 'Ow, I cut my finger, I need a *strip,' or 'Would you buy me a *strip at the store?', nor do companies advertise 'Buy our new *strips!' A typical puzzled response might well be 'A strip of what?' or 'What kind of strip?'
So we seem to need a descriptive term such as 'adhesive,' or 'bandage,' or both. In a written context such as a product description, something like 'adhesive strip,' 'adhesive bandage,' 'adhesive-strip bandage,' 'strip bandage,' 'bandage strip,' 'individual bandage,' 'individually wrapped bandage,' etc. should work.
In everyday language, of course, we're probably back to 'plaster' (BE) or 'band-aid/bandaid' (AE, one of those brand-become-generic terms like kleenex), which is what smaller adhesive-strip bandages are normally called.