How can I send an invoice to a participant, manually, without double sending
daveawe12323, welcome to stack exchange civicrm.
There are two ways of sending notification to user

Send Event receipt.

When you edit the participant using backend participant form, you should see 'Send confirmation' option. When checked the participant will receive receipt about the event having details of event and payment. But no activity will recorded in the system when a receipt is send.


Send Tax invoice

If you have 'Tax and invoicing' enabled, than you can create a invoice on the payment. You can download the invoice and send via email or you can email the invoice from CiviCRM. Both the option will create activity in Civi to track when the invoice was downloaded or emailed.