2 valid visas H1B and C1.What should I do?

I am Indian working in Chile. I have C1 visa already. I have applied for H1B and I got it stamped in Chile very recently. Now I want to go back to India before joining new job in US with new H1B. So when I travel from Chile to India(through USA) I will be having both C1 and new H1B(H1B never used at port of entry before as it is stamped just now).

What should I do>

  1. If I say, C1 at port of entry as it is transit visa. Will I have any problem as I also have H1B and not using it(Will I lose it and do I need to go to US consulate again for stamping)?

  2. If I say, H1B at port of entry and leave US the very same day , will there be any problem?

As the purpose of trip is transiting through US, you should use C1 visa and not H1. Using C1 would not impact your H1 visa stamp. Make sure PoE officer uses the right visa.