Hi @Graham 

Well my first thought is to write a E natural (no accidental).. because in your first sentence you said the song is in the key of F# minor.  The relative major of this key is A major.  In either key, the E is played and written as a natural (refer to the circle of fifths).

But then in the description line of your post, you are asking about how to notate a chromatic run ("Is there a convention as to how to notate a chromatic run?"), which if I understand your post correctly, this is a completely different question than how to notate a F#min/A maj scale.  The chromatic scale itself has no set notation, that is, there is no key signature for the chromatic scale.  However, notes written chromatically are notated based on the major/minor keys in which the piece is written, AND whether the notes are ascending or descending.  In general, the chromatic scale is usually notated with sharp signs when ascending and flat signs when descending.  But to avoid confusion, the composer will refer to the key of the piece for the correct notation (exceptions explained below).

However your post does not indicate you are writing for a chromatic scale, and you are discussing or hinting toward a harmonic scale, which is another topic altogether.  Harmonic minors DO change how the piece is written and played.  The harmonic for F# minor is written and played with a E#, so as to differentiate that it is harmonic and not a natural minor.

Additionally, the notes F and E# are NOT the same tones, at least on string instruments.  The piano plays these notes identical (it is the same piano key).  Violin (and the other orchestral string instruments) use tension and release intonation, which is something achieved differently on keyboard instruments. 

It is important to know what sound you want to achieve when you add this part to the music because the notation will communicate what sound you want.  If you need to emphasize the harmonic of F# minor, you can write in a E#.  Whether this is perceptible to the ear will depend on the player (it can be played slightly sharp).  There are some gypsy and Arabic based music in which the E# is perceptible and preferred.  The instruments and technique used to play this style of music are suited for this sound.  This tends to be quite dissonant, or harsh sounding, but that is the style of the music.  I am not sure if this is what you want to achieve with the folk music you are playing.  Also, it is not commonly written this way and is unconventional, but you can write this any way you want, assuming the theory is sound.

Not having the music in front of me and just going on the excerpt you describe, it is difficult to give you precise answers.

So I am just slightly confused by your question, but I hope that I was able to cover several areas to help you.

(All... if my understanding of theory is lacking, please feel free to correct me.  I welcome any input)