Better.

To me, "encountering" sounds ambiguous here. 遭難 isn't used to mean "to stumble upon / discover / encounter a ship at sea that is in distress," for example. Maybe "meeting with" works better.

@@ -20 +20 @@
-<gloss>(encountering a) disaster</gloss>
+<gloss>(meeting with) disaster</gloss>

It's an interesting nuance which the JEs evade. Perhaps this is closer.

@@ -20,2 +20,2 @@
-<gloss>disaster</gloss>
-<gloss>accident</gloss>
+<gloss>(encountering a) disaster</gloss>
+<gloss>(having an) accident</gloss>

I think it says it's a noun because it describes the state of encountering a disaster 「災難にあうこと」. Dictionaries don't say it means just 災難. It's the same with all nouns to which you are allowed to put する to. For example 勉強: the act of studying, 勉強する: to study. I think the current glosses are missleading and it's a pretty common word so beginners who don't use monolingual dictionaries won't know the true meaning of the word and won't know the difference between 遭難 and 災難.

GG5: a disaster; an accident; a mishap; 〔船の〕 (a) shipwreck; distress.
	～する meet with 「a disaster [a mishap, an accident]; 〔船が〕 be wrecked; be in distress.
中辞典: a disaster; an accident; a mishap; 〈船の〉 (a) shipwreck
	¶遭難する meet with ┏a disaster [an accident]; 〈船が〉 be in distress (難破･沈没の危険にさらされている); be wrecked (難破している); 〈船員･船客が〉 be shipwrecked
Daijisen: ［名］[スル]災難に出あうこと。特に、登山や航海などで命を失うような危険にあうこと。「冬山で―する」

Daijisen says it's a noun.
I think the original set of glosses were fine.

@@ -20,2 +20,5 @@
-<xref type="see" seq="1198180">遭う・2</xref>
-<gloss>to encounter a disaster or accident</gloss>
+<gloss>disaster</gloss>
+<gloss>accident</gloss>
+<gloss>mishap</gloss>
+<gloss>shipwreck</gloss>
+<gloss>distress</gloss>