If you have the urge to laugh and try to stop yourself but make a slightly sneaky noise with your throat for a second, without smiling, does that break your prayer?
Salam. Well in your case the "slightly sneaky noise" resulted from the :urge to laugh". Thus you had the intention to laugh but could not control yourself to such an extent and that noise came out your throat.
Well according to this view (hanafi) which I follow is that there are a couple of conditions when laughing during the salah. (1) Smiling does not invalidate the prayer whatsoever. ----- al-Mawsoo’ah al-Fiqhiyyah, part 27, p. 124.
(2) If one was to laugh and a person that was praying right beside WAS ABLE to hear it, then your salah breaks and must be repeated (since it becomes wajib after initiating any salah). Also your wudhu breaks.
(3) If one was to laugh and a person that was praying right beside WAS NOT able to hear it, then the wudhu does not break but the salah does. This is called dahk. The salah must be repeated.
Note: I believe in the Shafii' madhab laughter only invalidates the salah and not wudhu ... check up on that.
Laughter is known as one of the things that nullifies ones Prayer, as it was narrated by Jaabir Ibn Abdillah (may Allah be pleased with him) who said:
"If one laughs in their Prayer then they should repeat their Prayer and not their Wudu."
Related by Ad-Daraqotni: (51), and was authenticated by Ibn Hajr in Fath Al-Baari: (1/336).
According to my reaserch (in the site below):
This type of laughing according to what you explained that if you have the urge to laugh and try to stop yourself but make a slightly sneaky noise with your throat for a second, without smiling, does that break your prayer, does not look invalidate the salat as a quite quiet laughing, but apparently it invalidates the salat if you laugh loudly and on purpose.