H4 to H1 COS travel from India to US

We had to travel to India a couple of days back due to a family emergency. My spouse is on H4 till September 30th and she has a valid H1B petition approved and the status will change to H1B on October 1st. We are planning to travel back to US on Sep 27th or 28th. We dont have the approved H1B petition yet with us, since we could not receive it from the employer before we travelled to India. On reentry to US, she will enter on H4 but will have only very few days (3 days) left on her H4 visa validity based on our existing H4 petition in hand. (Expiring exactly on September 30th). Will this cause any problem at the port of entry? Does she have to show any additional documents related to her upcoming H1B?

She will receive a new I94 and hence you should apply for amendment on your approved H1. This can get complicated. Best way is to have your spouse stayback, get H1 stamped and travel back. If her H1 gets denied then she can travel back on H4. Especially when her H4 is also expiring not a good idea to take the risk.