FLR until I wait for Cos

[mrcool123]

I have been in the UK for 3 years now. I was made redundant at the start of this month. My current skilled worker visa is expiring by the end of this month. I have a job offer from a company, but they are in the process of acquiring a license for sponsorship. They might be able to give the COS by early January. I could have travelled back to India and returned back in January once I got the new visa. However, my daughter, who is my dependent, would miss school, and as she is a special needs kid, the whole change could be difficult for her to handle. Could I possibly opt for FLR for the time being and continue to stay in the UK and apply for a new skilled worker VISA in mid-January? This would even help in not resetting my clock for ILR.

Would going via the FLR route (suggested by an immigration solicitor) be the right approach here?
Would this cause any issue later on when I apply for ILR?