This depends on your level of literalism. The issue with the concept of 'Conquest' is that it implies a complete destruction and settlement, whereas the text never suggests this. The other issue is that the date of the Exodus is traditionally ascribed to 1446BC, which means the conquest took place around 40 years after that. There appears to be no evidence of them taking over the land unless you fiddle with the dates a bit, and sometimes the archaeology doesn't tally. If you take a more 'this story has roots in something, we're not sure what', then you've got space to investigate, and Kenneth Kitchen probably has the best 'This is how it could have happened' scenario. It is clear that for some reason, the Israelites 'won' over the Canaanites eventually, but the cause and origins of that winning is disputed. This has led some to suggest that the Israelites are in fact Canaanite in origin, (not Mesopotamian) as they believe the Exodus-Conquest cycle to be nothing but a fiction. Others think there's a kernel of truth in there, and like most ANE documents, you have to pick your way through it.

But in answer to your question, the only clear external record from other people are at the wrong date. The only mention of Israel is in Merenptah's stele (circa 1206) where he describes

"Israel is laid waste and his seed is not; Hurru is become a widow because of Egypt"

(all ANE accounts of destruction should be taken with a large piece of salt, so ignore the 'laid waste' part). If the 1446BC Exodus is correct, then we've got a problem in that there is no mention of this attack on Israel in the 1200s according to the Hebrew text, assuming they were interested in recording it at all (if indeed Israel of 1206 is the same Israel). Regardless, it's past the traditional conquest dates of circa 1400BC, unless you want to choose a later Exodus date (which ranges from 1200-1000, depending on your author). Either way, there's nobody talking about Israel.

That silence shouldn't necessarily be taken to mean anything however. The majority of the nations around Israel tend not to talk about their neighbours at all. To recycle an old comment, no Assyrian source names anyone in Philistia, Transjordan, Israel (north or south) or Phoenicia between 1200-1050). Of the remaining sources of perhaps lesser powers, most of them are concerned with their own local affairs - the neo-Hittite kingdoms make no mention of Canaan or Phoenicia. No Aramean inscriptions exist from before the 9th century save Tell Dan and Melqart, and no administrative texts either. Phoenician texts tend to mention only their own kings, and they tend to start only around 1000 BC. It could simply be that there were references but they are all missing, but equally it might not. The only possible link might be if you take the Israelites to be some sort of Habiru which are mentioned in the Armana letters. That is quite tantalizing, but it really doesn't quite fit (cf Anson Rainey).

So if there was an Israelite contingent who moved into Canaan, there's nothing written about them unless you count Mereneptah's comment, and that says nothing about the conquesting.