You aren't asking your contacts to delete WhatsApp as well in solidarity or to fully "switch", you are asking them to simply use Signal to communicate with you. If you mention you are uncomfortable using WhatsApp, and they aren't willing to use Signal to message you, they likely aren't worth talking to.
I deleted Facebook/Messenger awhile ago, and asked that people use Signal to communicate with me. All of the people I cared to speak to use Signal to message me, and many of them have used it for other purposes as well. That hasn't precluded them from using whatever they were using before. This only applies to the personal sphere of my life, conducting business with WhatsApp may be a different issue entirely.
I deleted Facebook/Messenger awhile ago, and asked that people use Signal to communicate with me. All of the people I cared to speak to use Signal to message me, and many of them have used it for other purposes as well. That hasn't precluded them from using whatever they were using before. This only applies to the personal sphere of my life, conducting business with WhatsApp may be a different issue entirely.