I don't want to turn in to DiyNutJob but I cannot recall experiencing it when I used to use the official Dell barrel charger
As long as the charger is a legitimate brand and CE marked, there is little to worry about - the class Y cap will pass a touch current of a fraction of a mA.
This tends to be a 'thing' when aftermarket chargers are used.
For example, the official charger for the Unibody Mac, appears to be Double Insulated, but has a kOhm resistor connecting the earth to the Gnd in the PSU and several high value resistors connecting the Gnd, to the body of the laptop.
I've experienced the tingle on Macs with aftermarket PSU and even with an official PSU, that has been used with a 2 pin plug adapter.
The OEM parts are also often better specified, with tighter control of components (adding cost), allowing for an acceptable touch current whilst minimising RFI - especially true if the appliance is a medical device.
It's unlikely that any component is failing, or the device is dangerous; its more likely that the OEM part is better specified and it may also have had a link to the earth - most of the dell laptop chargers I have dealt with have a cloverleaf 3 pin mains connector on the power brick.
Edit:
1KOhm earth to Gnd on a Dell USB-C charger, I have here...