Unfortunately you have no good solutions here.
There is no reason why the shifting should not work with a missing sprocket, you just have to get the indexing correct. The jump from 19 to 23 may be poor though. You may be able to prevent the shifter from shifting off the truncated cassette by winding the low limit in. This is obviously a kludge and you are missing a gear ratio.
You can't use a 10 speed cassette because the spacing of the sprockets is different on 10 and 11 speed cassettes. Also 10 and 11 speed chains have different external widths. See http://blog.artscyclery.com/science-behind-the-magic/science-behind-the-magic-drivetrain-compatibility/
Shimano retained the 10 speed freehub body width for 11 speed MTB groupsets. The reason this works is that the large inner sprockets can overhang the spoke flange slightly. Some Shimano 11 speed road cassettes can also do this, but they are all wide range models with 36 tooth or more (I think) large sprockets.
If you have a 5800 SS (short cage) derailleur the max large sprocket is 28, is you have a GS (medium cage) the max large sprocket is 32. See https://productinfo.shimano.com/download/?path=pdfs/archive/2017-2018_Specifications_v028_en.pdf, search for 'RD-5800'.
Really the only proper solution is to get a a wheel with an 11 speed hub.