COS to H1B while primary H1B holder applies for H1B transfers

[COSToH1B]

Hi,

My wife is primary H1B holder and I am on a dependent visa (H4) right now. I have already received an offer from a US company which has applied for COS from my H4 to H1B. The state of the application is initial review.

Now, meantime my wife has received a better job offer and wants to transfer her H1B to this new company.

My question is - Do I need to transfer my H4 to this new company as well... or simply wait for my H1B result?

If I do not apply for H4 transfer, what is my status till my H1B decision is made?

If I do apply for H4 transfer, will it cause any issues in my H1B processing as I have given copy of my old H4 to USCIS?