What techniques are available to dig a perimeter in the Nether without glitches/cheating?

I know of three decent techniques.

One is pretty risky, expensive, messy, but requires little effort (providing you have a good wither skull farm). Making the perimeter is extremely easy. It's the cleanup afterwards that may create some problems.

In short - you spawn a lot of withers under the bedrock, then you afk for a long time above the bedrock until all blocks are cleared. Then the hard part comes - you manually kill all the withers. Video about the process:

The other approach is to dig down to the lava lakes level manually, then build the bottom part of a world-eater - just the sweepers part, with a simple attachment that replaces the entire upper part moving the stations and sweepers a block down on player's request - and launch it manually after lowering the "land" level by 1, to sweep up all the remaining lava.

The third approach is very expensive in terms of iron (3 ingots per 1 source) but if you have a very good iron farm, it's not a problem. Quaff a fire resistance potion, fill your inventory with empty buckets, and hold rightclick at the lava lake. Since lava buckets are unstackable, 15 out of 16 buckets will land in lava. Tweakeroo is very helpful providing replacement of depleted stacks of buckets in your hotbar, and Itemscroller helps crafting bulk amounts of buckets. It's the fastest way of getting rid of lots and lots of lava "manually", but expect a couple shulkerboxes of iron blocks to go into lava.

It's easier to drain lava lakes using Sand. Or any other gravity block, as @Diehe suggested. And you will need A LOT of it, because those lakes can be deeper than expected.
You may need several Shulker boxes to transport all that sand blocks.

I found this video months ago that could be useful for you.

For lava lakes I recommend lots of gravity blocks such as gravel and sand. Fill it in until you've filled up what you need, you can then remove the blocks. In the overworld, try sectioning it off with gravity blocks, about 5 blocks between each border. Place sponges in between the borders to clear the water. You can go to the Nether and place all your sponges to quickly dry them. You will also want an elytra, it makes most things easier.

I recall the people on the ZipKrowd server using vertical shafts filled with TNT and sand to clear a perimeter for a wither skeleton farm. They probably used sand/gravel for the lava as stated by Diehe, but you could just as well use flying machines to clear the lava. IIRC this is how world eaters deal with water. An elytra will most certainly be helpful to remove the odd leftover block. I'll update this answer with the video if I can find it again.

EDIT: Found it. Around 7:20, you see the shafts in the open. Turns out they used netherrack and not sand to pad the TNT.