To run .NET applications (written in C#, VB.NET, ...), you never need Visual Studio. You'll only need the
.NET Framework[
^].
But if your application uses SQL Server for database transactions, you will have to install it anyway (you can install
SQL Server Express[
^] on the other system), or make sure you have access to a system that has SQL Server installed. If you have, then your application can connect to SQL Server on that system and perform database transactions that way.