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Very interesting plan. But I'm afraid it's impossible partially, with regard to external SIM card reader.

The SIM reader lanes are routed to the wwan modem connector directly, not via any bus. Whereas laptop port, assuming USB port, is connected to USB bus, then to one of the SoC' (or PCH') internal USB hub and the USB port. Isn't it? 

I know about external SIM reader for wwan modem in PCIe-mini form factor. I know about extension for micro/nano SIM reader with flat cable which is inserted  into the reader directly. But this isn't your way IMHO. 

What about Lenovo genuine SIM tray for X1C Gen7? Its p/n is 5M10V25491. I see this part on aliexpress but it's extremely overpriced. May be you'll find it elsewhere, for instance, Lenovo Authorized Service Providers.

Hi Tequilacheeto, That model definitely doesn't have WWAN, nor does it have provisioning for it, so the best option is a USB WWAN dongle.

The model is 20R1S04100 and i don't think that it comes with one. At least I cannot see it after opening up the laptop.

...

Does the reader still exist on 20R1S04100?

Unfortunately, the parts list of X1C Gen7 doesn't allow to determine whether the nano SIM card reader soldered to the systemboard depending on the MTM.

Take a look at the image linked below, the bottom edge of the PCB. There is a nano SIM reader. 

Now take a look at the laptop rear side, its center. Is there a dummy at the reader' place (follow the laptop User Guide if you have some difficulty where it should be)? I'm afraid the surface of the case is smooth, w/out a dummy. It might mean the nano SIM reader is absent as well.

So, probably the best solution in your case is to use mobile LTE/WiFi router. It has some advantages in comparision with hotspot on the smart phone as well laptop USB dongle.

https://download.lenovo.com/Images/Parts/5B20W21729/5B20W21729_B.jpg

There are many featured reliable mobile LTE/WiFi routers on the market by a lot of manufacturers. Most of them are based on the chips of Huawei, Qualcomm etc.

Good catalog with their models, specs, reviews is below

https://www.4gltemall.com/4g-wireless-router.html

Fortunately, left column shows the manufacturers by their devices popularity. Choose from the top Huawei to Novatel, it's enough.

Don't pay an attention for the prices on that catalog, they aren't even manufacturer' recommendable, i.e.too high against the market.

The device choosing depends not only on its availability. Main feature you have to know is the LTE frequency bands set the device supports. They should match to the ones your LTE cellular operators work in. This task seems not easy for non professional, so, you might list the operators here, I'll try to reply about their LTE networks.

Next important features as you'll see are the DL/UL speed, LTE Category. In most cases mobile 150 mbps might be enough. Or you may need higher speed. Anyway, don't choose the devices which feature up to Cat.4 only. They are too old. Cat.6 and higher is right choice.

The battery capacity, the WiFi frequency and modes are other features. Usually these devices use their USB port for a power connection and battery charging only, i.e.not for a data transmission. This might be the only inconvenience.

Most devices could be easy unlocked, so cheaper operator's device might be one of the choice either.

As an example of good device - Alcatel Y900 / Y901. But again, take a look at the frequency bands firstly.