Can you use a cfn param in appsync construct custom domain config

[mrllama123]

Hello i was wondering if any one has had any luck with trying use cfn parameter of type ssm in the domainName property of the appsync construct similar code to this:

// used code from: https://docs.aws.amazon.com/cdk/api/v2/docs/aws-cdk-lib.aws_appsync-readme.html#custom-domain-names

import * as acm from 'aws-cdk-lib/aws-certificatemanager';
import * as route53 from 'aws-cdk-lib/aws-route53';

const zoneName = StringParameter.valueForStringParameter(scope, '/<param name>'
const certificateArn = StringParameter.valueForStringParameter(scope, '/<param name>')
this.hostedZoneId = StringParameter.valueForStringParameter(this, '/<param name>')

const myDomainName = `api.${this.zoneName}`

// cert arn is defined in another stack
const certificate = Certificate.fromCertificateArn(this, 'certificate', certificateArn);
const schema = new appsync.SchemaFile({ filePath: 'mySchemaFile' })
const api = new appsync.GraphqlApi(this, 'api', {
  name: 'myApi',
  definition: appsync.Definition.fromSchema(schema),
  domainName: {
    certificate,
    domainName: myDomainName,
  },
});

// hosted zone for adding appsync domain
const zone = HostedZone.fromHostedZoneAttributes(this, 'hosted-zone', { hostedZoneId: hostedZoneId, zoneName });

// create a cname to the appsync domain. will map to something like xxxx.cloudfront.net
new route53.CnameRecord(this, `CnameApiRecord`, {
  recordName: myDomainName,
  zone,
  domainName: api.appSyncDomainName,
});

I'm trying to make my cdk stacks environment agnostic as right now i have hardcoded the hosted zone name and certificate arn in the cdk stack config