Selling a B2B SaaS product in the U.S as a U.K company – A tax nightmare?

We have great traction in the U.K and have been experimenting with U.S markets for the last few months. The feedback has been great and we're seeing early signs that it will be a great market to pursue.

However, I am conscious of what tax we will be responsible for.

From doing initial research, it seems I won't have to register as a U.S business and pay any federal tax as we don't have a 'nexus' within the U.S. We won't have an office or employees, everything will be operated from the U.K as it currently is.

It seems like the only tax we have to worry about is sales tax, however, quite a few states do not have sales tax on SaaS products.

If we are only focusing on these states that don't have sales tax on SaaS and we don't have a U.S nexus, are we good to go without worrying about tax?