We are using option 1 and have had good experience with it. We have informed the users and waive another mandatory field. No customizing, if not absolutely necessary! Our users write a work detail with the missing CI information.
We check it weekly, evaluate the value for the CMDB and supplement the CI if necessary.
This is also the advantage over option 2, where users without an eye for the CMDB can add elements that you may not want to have in.
You could also impose a more heavy handed approach of forcing users to submit a CI Discrepancy incident with the CI data required, and the CI could be created based on that incident, then it can be associated with the CRQ. This approach may be percieved as slowing down the CRQ creation procedure but users will quickly learn that they must ensure the CI exists before creating their CRQ.
That said, I have also seen your option 1 implemented. The downfall of that option is that for up to a month (if you're checking only monthly), your CMDB may be out of date, even if the problem (a missing CI) was identified on day 2 of the month.
Lastly, you can always implement the heavy handed approach, and if heavy resistance occurs, then implement your option 1. Point is, you don't need to lock yourself in forever with a solution. Five yourself the freedom to try something and if it doesn't work, implement something else.
If you are treating your CMDB as centralised repository then that particular CI must be available. both the suggested options will result in data inconsistency/duplicacy and at the end outdated CMDB.
In your situation, I would suggest below approach:
Create some generic business services CIs which can be used at the time of CR creation. (in absence of actual CI). additionaly users can create incident saying particular CI is not found and it will be assigned to Asset Management Team. This Incident will be attached to original CR. Asset team will create/update the CI based on information provided in incident. Once the Incident is resolved, Change Coordinator/manager will related that CI to the actual CR.