If you have centrifuge facility in animal house, you can carry them in media (preferably in ice can keep all cells alive). Since plastic vessels we use does not have coating, cells won't get attached to walls but clumps might form which can be removed by re-suspending them before injection. Before injecting into mice PBS wash to cells is required as usual.

Thank you for your reply. We don't have centrifuge in animal facility.

If I was in your place, I would seal the culture dish with Parafilm first to avoid any contamination and keep at ambient temperature (close to 37 degrees). Perhaps use thermocol for insulation. Avoid excessive shaking.

Hope you get more suggestions on this. Good luck!