Listings on major exchanges does often come with big players where there's a lot of tokens in circulation so dumps are unavoidable, so it can have its advantages. While listing only on small exchanges can be a sign of weakness for a project - considering that teams often aim to have their project listed in the best places possible. To me it often seems like the latter, but this is my conservative approach and can't say that it didn't do me well.
Since OP wants to invest in early projects, I think that scenario and setup should already be taken note of by the OP.
What OP care about is how safe those small exchanges are against hacker or something sh*t. Generally, there's no 100% protection against hackers but at least these exchanges, big or small, are doing their best in terms of security.
If only OP can tell us some examples of
"small exchanges", we can give a much accurate response like the reputation of that said exchange.