I assume Schnürlischrift is the Swiss-German equivalent of what elsewhere in the German-speaking world is known as Schreibschrift. I‘d have called it joined-up writing too, but LEO calls it cursive: Siehe Wörterbuch: Schreibschrift

From NZZ.ch: Auf dieser weissen Tafel mit dem grauen Rand lernte man «verbunden» schreiben, die sogenannte Schnürlischrift (hochdeutsch: Schreibschrift).

At least according to Wiki, that would just be what we (AE) call "cursive writing."

https://en.wikipedia.org/wiki/Cursive

Cursive (also known as script, among other names[a]) is any style of penmanship in which some characters are written joined together in a flowing manner, generally for the purpose of making writing faster, in contrast to block letters. Cursive handwriting is very functional, and is intended to be used in everyday writing. In addition, it is also used in art and calligraphy hand-lettering. Formal cursive is generally joined, but casual cursive is a combination of joins and pen lifts. The writing style can be further divided as "looped", "italic" or "connected".

@hbberlin: Might this be another AE/BE difference? As mentioned, I‘d have called it joined-up writing, whereas neither cursive nor script would have come to mind. I remember, too, that in the Harry Potter series Gilderoy Lockhart at some point says „I can do joined-up writing now“. Maybe US-based readers can recall whether this expression was also used in their edition.

I, BE, late 30s, would call it 'joined-up writing,' but my daughter, 8, also BE, calls it 'cursive' !!!

If you google KS1+cursive (KS1, or Key Stage 1 = primary school Years 1 & 2 = ages 6-8, the two years of primary school when children will typically learn cursive) you'll see that that's the word in use in UK curriculum nowadays.

This isn't necessarily helpful for the OP, since it doesn't reflect current usage among the over-8s (!), but just to say that 'cursive' is the 'correct' terminology in education (now).

Falls es schriftliche Belege für "joined-up writing" oder sonstige englischsprachige Bezeichnungen gibt Siehe auch: cursive - script - Schnürlischrift, f [Schweiz] ...

:-)

My children all learned Schnürlischrift at school here in CH. As a distinctly over-8, I would still simply call it "joined-up writing" even tho' I am aware of cursive writing as opposed to block letters.