To my experience, if the chain drops on 1xX conversions (just running the middle chain ring) depends of course on riding style, but a lot also on the rear derailer. You have to found one or adjust that this is keeping the chain tight. A proper chain lenght, rather short, helps also a lot.
Instead of an still a bit expensive NW chainring I'm using at some 1xX conversions an bash guard at the outer position and sometimes an anti drop clamp on the inner side.
Something like this
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but it depends on the frame is this fits well enough to do a proper job.
Different topic: as a lot of the old cassettes, especially also 7 speed have very limited bandwidth, e.g. just 14 to 28.
That's fine for completely flat ground, for me ideally with a 38 or 40T front chain ring.
Just in case you need a bit more flexibility for short uphills or higher speed, or if the cassette has anyhow a lot of wear. There are nowadays also 12-32 cassettes for 7 speed, which work well also with old rear derailleurs, giving then a bit of more broad choice for gear ratios.
For 8 or 9 speed set-up I'm using always 11-36 cassettes, because this gives a nice choice but still works with all old derailleurs.