SQLite is very good with read performance. 10,000 visitors should be quite easy considering the numbers shared by the official SQLite team’s when-to-use-sqlite. As per their statement, SQLite should be capable of handling upto 100,000 hits/day without a fuss. However, you need to take into account: the hardware plays a key role here as in most other databases.
As a final word, You should be good with SQLite for handling 10,000 visitors a month.