It works!
We have a super suportive IT department and they made me a full disk backup after which I went on installing Ubuntu. And the installation is a success. Dual-booting in both Windows 7 or Ubuntu.
First I started the laptop as usual and booted under Windows. I then plugged in the USB stick with the Ubuntu installation image (Ubuntu 12.04.4 LTS) and rebooted the machine.
While in the reboot process I pressed F12 (or F10 can't remember) to "pop up" the boot menu to choose the boot device. I choose "UEFI USB Flash Drive" (or equivalent name). Ubuntu started up and I choose to install it. I partitionned manually the available space and it a standard installation.
After installation, the system rebooted but I got directly into Windows, no Grub promt. I perhaps miss configured the boot loader during manual partitionning (surprisingly as I had explectictly chosen sda, but anyway). I rebooted again on the USB stick and did mount the new /boot
on sda and installed the Grub boot loader using this resource. Rebooted again and this time everything was as expected.
I have selected Windows as the default boot (required by the IT department), and I do not need to enter twice my credentials (at boot prompt to unlock the disk, and then again to login to Windows, I only need to do it at boot prompt). But just after entering the boot prompt credentials (to unlock the disk) I can switch to Ubuntu if I would wish to.
So it has been working perfectly :-)