To use STLink-V2 without a reset connection you must edit the debug script. For that you should select “Use local script” to reference your script, instead of keeping it auto-generated, thus it will not be modified (go to the “Debugger” tab of the debug configuration to change the radio button from “Manual spec” to “Use local script”).
You should probably also rename the .custom.cfg script name to some name that does not start by a dot, so that it will be more visible. If you do not see this file name (nor .project or .cproject) in your project you should right click on the small triangle at the top right of the project explorer window, select “Customize view...” and uncheck the “.*resources” line, like in the screenshot below).
Hope this helps,