I do this kind of thing when making ukulele sides (though mine will be around 70mm wide). I'm planing down to around 1.8mm, where the wood becomes really flexible.
The best way I've found is to take a piece of melamine faced chipboard (standard shelf material) and glue two guide strips on it which are just higher than my final thickness. I place these around 10mm further apart than the width of the strip I'm planing.
Clamp the strip between the guides at one end (leaving 0.5mm each side) then plane away from the clamp. Angle the plane at 20 or 30 degrees so its sole rides on the guide strips either side while the blade cuts the wood itself. Swap the strip end for end regularly so that you gradually take it down - it's easier to take a little off each end at a time. Take thin shavings.
This works nicely in non-figured woods which don't have a lot of runout. With light runout, a close set cap iron should mean only a little tear-out when planing against the runout (this is why I set my guides a fraction higher, removing the last 0.2mm or so with a cabinet scraper). Heavy runout might mean this method doesn't work.
200 mm strips are short, so I'd probably use a block plane for those - harder on the hands, but less unwieldy. My ukulele sides will be nearer 400mm. so I can use a bench plane.
For figured woods I'll place the strips further apart and plane across the grain at 45 degrees using a close-set cap iron. The heel and toe of the plane need to stay on my guide strips so I can only take very short strokes. For this I clamp either end and plane the middle, then move one clamp to the middle and plane the free end, then swap the end clamp and plane the other free end. I'll regularly rotate the strip so i'm planing it from either side. Doing this is likely to cause tear-out on the side towards which you are planing, so leave a little extra width and trim the strip down once it's at final thickness to remove this. With this method I spend nearly as much time removing and refitting clamps as planing, but it's worth the time to save destroying highly figured wood. As before, the final fraction is removed with a cabinet scraper.
I have used the superglue and masking tape method successfully, but found clamping as described is easier for me.