Verification-done on xenial:

dkms 2.2.0.3-2ubuntu11.6

Upgraded kernel to hwe kernel, drivers can still be loaded from the right versioned directory for the kernel and loads succesfully -- signature is validated fined as the kernel module is signed.

ubuntu@ubuntu:~$ dpkg -l shim-signed dkms | cat
Desired=Unknown/Install/Remove/Purge/Hold
| Status=Not/Inst/Conf-files/Unpacked/halF-conf/Half-inst/trig-aWait/Trig-pend
|/ Err?=(none)/Reinst-required (Status,Err: uppercase=bad)
||/ Name           Version                                       Architecture Description
+++-==============-=============================================-============-==============================================================
ii  dkms           2.2.0.3-2ubuntu11.6                           all          Dynamic Kernel Module Support Framework
ii  shim-signed    1.33.1~16.04.4+15+1533136590.3beb971-0ubuntu1 amd64        Secure Boot chain-loading bootloader (Microsoft-signed binary)
ubuntu@ubuntu:~$ sudo modprobe bbswitch 
[sudo] password for ubuntu: 
modprobe: ERROR: could not insert 'bbswitch': No such device
ubuntu@ubuntu:~$ dmesg | tail
[    7.551980] wlp3s0: waiting for beacon from fc:ec:da:3c:dd:85
[    7.654548] wlp3s0: associate with fc:ec:da:3c:dd:85 (try 1/3)
[    7.656500] wlp3s0: RX AssocResp from fc:ec:da:3c:dd:85 (capab=0x411 status=0 aid=3)
[    7.676864] wlp3s0: associated
[    7.676917] IPv6: ADDRCONF(NETDEV_CHANGE): wlp3s0: link becomes ready
[   17.687856] random: nonblocking pool is initialized
[  122.752094] bbswitch: loading out-of-tree module taints kernel.
[  122.752723] bbswitch: version 0.8
[  122.752745] bbswitch: Found integrated VGA device 0000:00:02.0: \_SB_.PCI0.VID_
[  122.752767] bbswitch: No discrete VGA device found


ubuntu@ubuntu:~$ cat /proc/version_signature 
Ubuntu 4.4.0-143.169-generic 4.4.170
ubuntu@ubuntu:~$ sudo insmod /lib/modules/4.4.0-143-generic/updates/dkms/bbswitch.ko 
insmod: ERROR: could not insert module /lib/modules/4.4.0-143-generic/updates/dkms/bbswitch.ko: No such device
ubuntu@ubuntu:~$ dmesg |tail
[    7.676864] wlp3s0: associated
[    7.676917] IPv6: ADDRCONF(NETDEV_CHANGE): wlp3s0: link becomes ready
[   17.687856] random: nonblocking pool is initialized
[  122.752094] bbswitch: loading out-of-tree module taints kernel.
[  122.752723] bbswitch: version 0.8
[  122.752745] bbswitch: Found integrated VGA device 0000:00:02.0: \_SB_.PCI0.VID_
[  122.752767] bbswitch: No discrete VGA device found
[  221.958525] bbswitch: version 0.8
[  221.958540] bbswitch: Found integrated VGA device 0000:00:02.0: \_SB_.PCI0.VID_
[  221.958554] bbswitch: No discrete VGA device found
ubuntu@ubuntu:~$ sudo hexdump -Cv  /lib/modules/4.4.0-143-generic/updates/dkms/bbswitch.ko | tail
00005740  40 ac 93 85 cb 5f 1e 3e  6b 7b db 62 86 66 ea 81  |@...._.>k{.b.f..|
00005750  1e 9a 9a 1e a6 05 dc e1  18 dd 27 40 27 42 31 9f  |..........'@'B1.|
00005760  fd 54 ac 4a f6 26 21 32  f3 b4 52 70 f4 79 a6 0d  |.T.J.&!2..Rp.y..|
00005770  c9 75 93 46 a5 2b ed fe  ef a1 68 97 c0 e0 67 c7  |.u.F.+....h...g.|
00005780  32 f7 4c c9 6d 0a 00 29  ce 87 a0 0a 95 be f1 4b  |2.L.m..).......K|
00005790  c3 2e 6b df 7f a5 b7 67  55 27 cb bf a8 ea 51 7b  |..k....gU'....Q{|
000057a0  a6 3e 00 00 02 00 00 00  00 00 00 00 01 a2 7e 4d  |.>............~M|
000057b0  6f 64 75 6c 65 20 73 69  67 6e 61 74 75 72 65 20  |odule signature |
000057c0  61 70 70 65 6e 64 65 64  7e 0a                    |appended~.|
000057ca