These Head Radical Pro II shoes are kind of marketed towards the racquetball crowd but they have non-marking soles and would be suitable for squash and other indoor sports.
Buy (Canada): sportsvirtuoso.com
Here’s another version in black & lime green:
Buy (France): amazon.fr
Buy (Germany): amazon.de
Here’s an all-black color I hadn’t seen before:
Image via Holabird Sports