Avoid Hardcoding Of UserId's in Apex

If you do not want the user id to be hardcoded as a string in Apex code then you should create a custom setting and then you can query the value in the trigger.

  Settings__c settings = Settings__c.getOrgDefaults();
  if (UserInfo.getUserId() != settings.SpecialUser) {
     //do logic for all users except the special user
  }
  else
  {
     //special user logic
  }

When the special user changes you can update the user id on the custom setting. Without modifying source code.

You could also use a Custom Permission and Permission Set to control access to a section of code. Create a Custom Permission 'Special User' assign to a permission set 'Special User Rights'.

  CustomPermission custPerm = [select id from CustomPermission where developerName = 'Special User' limit 1];

  List<SetupEntityAccess> access = [select setupEntityType, setupEntityId, parentId from SetupEntityAccess where setupEntityId = :custPerm.Id and ParentId IN (SELECT PermissionSetId from PermissionSetAssignment where AssigneeId = :UserInfo.getUserId())];

  if (access.size() > 0) {
     //execute special user logic
  }