How can I attach this message to a transaction when sending nothing?
If you send nothing, what are you going to attach it to?
Generally, for most tokens (the main EOS token included), the transfer action has a "memo" field which is exactly what you are looking for.
Sending 0.0001 EOS along with an advertisement text is a common pattern nowadays.
You can ...
Most of the testnet just uses the same fee and ram policy as the mainnet. On testnet, you can just easily ask for faucet tokens for your test.
The Junlge Testnet is the most popular one.
However, if you really need a network environment with cheaper fees and ram fees for any reason, you might want to consider implementing your own network with modified ...
How does one attach a message using a desktop wallet or cleos?
What is the max limit of the message?
How much does it cost to send a 1000 character message?
Answered here if you don't want to send EOS with your transaction, and here if sending EOS is acceptable.
What stops me from spamming the same message to every account and bloating the blockchain?