Normally, for RNA extraction, most of the kits are using lysis buffer first, then add ethanol for inactivation (Qiagen viral mini kit). So, I think whether the hospital could do these two steps. if you are using Trizol, you may need to add a carrier RNA into the sample, since the amount of viral RNA is low, difficult to get the RNA wo carrier RNA, but if you extract the host/cellular RNA together with the viral RNA, the carrier RNA is not necessary.

Not sure what lab you are talking about. Is it an in-hospital lab (e.g. another area of the same compound) or a remote lab? Why is inactivation in the hospital needed?

(see answer at the end)

First, i would like to add that handling of COVID-19 (and other infectious agents) specimens should be done only by trained personnel using appropriate PPE and a special circuit inside the building. The situation you are describing is quite dangerous for your safety and your patients'.

Since the lab has the means to extract and detect SARS-CoV-2 RNA, then they must surely have all that is needed for inactivation. Why is inactivation at the hospital so important? If the containers in which you draw blood are sealed (they should be), then there should be no problem in shipping them to the lab. In our hospital, the specimens are isolated in sealed plastic containers and shipped to the lab. This is true for the in-hospital lab and also for a secondary, remote lab. So far, we've had no problems with this system, nobody got infected and there were no accidents (e.g. spillovers). I would strongly recommend that you seal the specimens and ship them to the lab as they are. They will know what to do next and will have the equipment, training and circuits to do so.

However, if you REALLY need viral inactivation at the hospital, the only type of inactivation i can think about is by heat. All chemical inactivation would require you to process the sample that is uncapping the tube which would expose everybody. So heat it is then. Take a look at this article

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7271332/

During the extraction protocol in our lab, we incubate the samples with lysis buffer at either 56 degrees Celsius or 70, depending on the protocol, for 10 minutes. However, even without lysis, 10 minutes at 70 degrees C should inactivate the virus.

(it is still unclear to me why you need to inactivate at the hospital. Can you be more specific? Thank you!)

Different strategies are here for virus inactivation, like Photodynamic and photochemical sterilization etc.