For example, the gypsy scale, I-♭II-III-IV-V-♭VI-VII. Would you write a key signature for a scale like that, that didn't start on B♭ like scales are supposed to? Or would you just add the flat every time you play that note? Or would you choose the closest usable key signature and just add a flat/neutral to each note that was different? What if a scale has both flats and sharps, such as Hungarian I-II-♭III-♯IV-V-♭VI-VII?
Bartok did use some unusual key signatures for such scales. I don't know if it's a good or bad idea; much depends on how easy it is to read such a piece.
I would probably just find the major or minor key signature that minimized (or nearly minimized) the number of accidentals and use that. One might still change key signatures if parts of the composition are transposed. People can sight chromatically modified pieces pretty well. Short sections in a dominant key are not always resignatured (if that's not a word, it is now.)
Baroque signatures for minor keys are not hard to read and these seem a bit weird at times.
It's 2019; feel free to alter traditional notational norms in a way that's most fitting for your music.
Many composers have used non-traditional key signatures that don't follow the standard order of sharps and flats. And I've seen key signatures that use all kinds of accidentals, so don't be afraid to mix sharps and flats.
Here, for instance, is your gypsy scale based on C:
And here's your Hungarian scale:
If there is a clear sense of a root - perhaps the first note in your examples - then it might be easier for someone reading your piece if you use the key signature (whether major or minor) of that note and use accidentals for the other sharpened or flattened notes. But your first example could - assuming the first note to be C - be written with the key signature Ab Db, this order being as in a normal major or minor key signature.
Key signatures containing both sharps and flats may look a bit odd but they also exist. Your 'Hungarian' scale could thus have the key signature Eb-Ab-F# or F#-Eb-Ab. (It wouldn't have Ab-F#-Eb) By the way, in more complicated modes, for example D, E-quarter-flat, F#, G, A, B-quarter-flat, C#, there is the same problem: to show the quarter-flats in the key signature or just write them as accidentals.
[As a footnote I was going to ask where you got the names 'gypsy' and 'Hungarian' from.]
I would use the key signature corresponding to the root of your scale. Use the minor key signature if your scale has a primarily minor feel and the major key signature if it has a primarily major feel or is ambiguous about its major/minor tonality.
The reason for this is that clearly indicating the tonal center of your piece will make it much easier for readers to interpret it. Your piece will have lots of accidentals this way, but those are easier to read than a piece that makes it difficult to discern the function of different notes at a glance.
From a typographer's point of view, I would ask myself what the typical reader expects the most:
If it's a book about gypsy music, or a songbook of gypsy songs, or sheets for a gypsy band, I would stick with the non-western scale. Because here the reader expects to see a gypsy music.
If it's for someone else, maybe for a conventional band that will accompany you, or for a generic book or songbook or stuff, or a single short piece to be published seperately (maybe on the internet even), I would choose the most fitting western scale and use accidentals as needed. Because here seeing a gypsy key would confuse the reader and (maybe even more importantly) even make him play the wrong notes.
Note that especially with 2 flats for instance, people could automatically expect them to be Bb and Eb, without even checking the actual location of the flat signs in the staves.
Bottom line: As always in typography, choose one and stick to it; consistency is important, and here maybe even more important than making the right decision.
Would you write key signatures for non-conventional scales?
Yes I would, as it will be easier to me to write and to read it - and probably to others.
But I wouldn't use the Roman numbering like you did in your question.
For example, the gypsy scale, I-♭II-III-IV-V-♭VI-VII.
e.g. the gypsy scale I would notate as Phrygian with an augmented 7th and with relative names:
(I think I would even renounce an analyse in RN)