There are two main ways to do it - the natural way and the chemical way - and you already hit upon both in your post.
el natural:
Peat filtration, along with loads of driftwood, beech leaves, etc. will definitely lower your ph. If you want to get it really low, 5.0-5.5 peat is really the best option. I have fish that require 5.0 ph to breed, and for them i am planning to filter barrels of water with peat and use that water in my water changes for the main tank. It can be dangerous to simply put peat in your tank filter as it could cause the ph to drop too low or simply be too eratic.... low phs are rather unstable. You could start by adding just a little to your filter and monitering your ph carefully with a wide range test kit as you add more over the course of a few weeks. As you said, peat creates black water conditions in your tank, i.e. the water turns brown. If you are primarily concerned with the care and breeding of your fish, this shouldn't bother you, but I understand that it is not something many find attractive for display tanks.
chemical:
yes chemicals can be bad. ph up and ph down are unreliable, hard to dose correctly, and often only a temp solution. HOWEVER, buffers, on the whole, are great! I use proper ph 6.5 to drop my ph for soft water fish in all my south american tanks. The drop is permenant and the ph is very stable. The lable does say that it can be bad for planted tanks, but i have never had problems in my planted aquariums where I have used it. There are almost certainly plant safe buffers out there.
If you use a buffer, run some experiments with it first. I only have to use about 1/8th the given dose of proper ph to get its full effect on boston water - which has a very high ph - but is very soft. Harder water will be harder to manipulate and you may need larger doses, but using as little as possible is always advisable.
If your water is as hard as ours is at the store (millis/medway etc.) you will find buffers that lower ph and soften water largely ineffective. In this case you would either have to use RO water or use rain water.
A more important point than all this buffer ph talk is the nature of the wietzmani tetra. They are small, slow moving, reclusive tetras, and until they are well settled in, it is not surprising that they have not been out and about. They do come from dark waters and they don't like bright lights - you may see them more if you give the tank a twilight hour in the evening - if you add peat - or if you create dense undergrowth that darkens the lower levels of the tank.
I am not an expert when it comes to buffers, peat and planted tanks - but I have lived my hole life using bostons crazy water - and buffers and peat have both served me well. Do some research to find out what other people are using on their planted aquariums and do some experimenting to find out what works best for you
-Sam