SQLite- Read-only, low volume over network?

It is getting burdensome on my team to prototype tables in MySQL that back our Java business applications, so I'm campaigning to use SQLite to prototype new tables and test them in our applications.

These tables are usually lightweight parameters, holding 12 to 1000 records at most. When the Java applications use them they are likely to be doing so in a read-only capacity, and typically the data is ingested in memory and never read again.

Would I have a problem putting these prototype SQLite tables out on a network, as long as they are accessed via read-only and in small volume? Or should I copy them locally to everyone's machines? I know SQLite does not encourage concurrent access on a network, but I'd be surprised if more than one user would hit it a the same time given the number of users and the way our applications are architected.