I really don't want to use Amazon to send my emails. is there any option to use some other SMTP provider?
You can use SMTP from other email service provider. Here's a couple of other alternatives:
Please note that as Sendy is designed for Amazon SES, if you use other email service providers, bounces and complaints will not be registered. But these services may let you download emails that bounced or complained which you can then import into Sendy to mass delete or mass unsubscribed.
Here's how to use other email service providers with Sendy via SMTP:
Your emails will be sent via SMTP with the settings you've set.