Is it fair to assume that SHA1 collisions won't occur on a set of <100k strings I'm building a system that has to take file paths, and generate a unique name for each one. I'm planning on using SHA1 as the hash function.  My question is: do I have to deal with possible collisions (2 different paths producing the same SHA1 value) or can I assume it won't occur?
The chance of a collision in such a set is approximately $ \frac{1/2 \cdot n^2}{2^{160}} $, which for n=100k evaluates to about $ 3.4 \cdot 10^{-39} $. So it is fair to say, such a collision won't occur accidentially.

AFAIK nobody has ever found a SHA-1 collision The only concrete SHA1 collision to date was Google's on February 23rd, 2017 (found here). Collisions become likely once you generate about $2^{80}$ or $10^{24}$ hashes.

If cryptoanalysis advances, an attacker might be able to create inputs that deliberately collide. Currently, however, there is no known way to do this efficiently. Of course, this only applies if your application needs to protect against deliberate collisions; many applications only require protection against accidental collisions. If you need protection against deliberate collisions, I'd prefer SHA-2 over SHA-1.