Thanks to everyone who posted their suggestions on here. I too was having this problem with my Dell OptiPlex 7010 Windows 7 32bit PCs for Patches: KB4093118 & KB4103718.
I tried all solutions posted here but the one that solved the issue on my PCs was the HASP driver solution.
Using the Autoruns program I was able to see that the Hasp driver V4.65.1.1 was running on startup and after disabling it the patches install correctly and no more reboots. I then decided to check out the registry entry for "Haspnt"
HKLM\System\CurrentControlSet\Services\Haspnt
I noticed that the key labeled "ImagePath" had the data value of "\??\C:\Windows\system32\drivers\Haspnt.sys". I then tried removing the "\??\" and the patch worked afterwards, without having to disable from startup. Not sure if anyone else has that value
set but this might also help. For now I wont be updating the driver since this driver is only on about 40 PCs and most will be replaced soon.
I ran the following command/s in a script to test on a few machines to help disable to startup of the driver, rather than run Autoruns on all PCs
Disable on startup
reg add HKLM\SYSTEM\CurrentControlSet\services\Haspnt /v start /t REG_DWORD /d 4 /f
or to fix the ImagePath Value
reg add HKLM\SYSTEM\CurrentControlSet\services\Haspnt /v ImagePath /t REG_EXPAND_SZ /d C:\Windows\system32\drivers\Haspnt.sys /f
Thanks again to everyone who posted. hope that Peter can find his solution soon
5/29/18 EDIT: I will be performing the driver update. See follow up comment below for other issues I ran into with no driver update applied.