Assuming the customer ID doesn’t need to change with the access token, a good approach to your concern is to use custom attributes and attach them to access tokens. Documentation on doing that can be found here. The idea is that, through this way, only the access token needs to be passed in with API calls. Then upon using VerifyAccessToken (or getOAuthV2Info policy) Apigee Edge will extract the customer ID.
After VerifyAccessToken, the custom attribute can be accessed via accesstoken.{custom_attribute}. After getOauthV2Infopolicy, the custom attribute can be access via oauthv2accesstoken.{policy_name}.accesstoken.{custom_attribute_name}.