Currently, this redirection can't be done using verification link in email. I tried adding redirect_uri to the verification URL a while back but they do not work.
Workaround
I know this is a convoluted workaround for such a simple requirement. The best way would be to raise a feature request and hope they support a redirect_uri in the Cognito URL.
EDIT
To save your lambda costs, you could also use an HTTP endpoint in your API and make a request to the cognito service endpoint for your region. Example:
POST HTTP/1.1
Host: cognito-idp.us-east-1.amazonaws.com
x-amz-target: AWSCognitoIdentityProviderService.ConfirmSignUp
Content-Type: application/x-amz-json-1.1
{
"ClientId":"xxxxxxxxxxxxx",
"ConfirmationCode":"123456",
"Username":"username"
}
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