While not a particularly loud keyboard, there are a few options for quieting the HHKB line, including stock models with built-in silencing rings and aftermarket modifications.
Lubricating a Happy Hacking keyboard can lead to pretty dramatic reductions in sound, both for standard keycaps as well as stabilized keys, depending on the choice of lubrication.
Lubricating tends to help mitigate some of the higher-pitch plastic-on-plastic and metal-on-plastic sounds produced by the sliders and/or stabilizer assemblies making contact with the top case or other internal components.
See Lubrication for more details.
There are a number of options for aftermarket silencing rings that replicate the function of Type-S silencing rings.
These rings absorb the impact of the slider when it makes contact with the housing after being pressed and returning to the unpressed position.
Deskeys provides a fairly wide range of options to suit various slider types and desired volume reduction, including 'Ultra-thin' and 'Thin' models backed by the claim of 'minimal travel reduction' on standard, non-Type-S sliders. They also produce translucent white silicone silencing rings, which might provide a different sound profile compared to their classic black silencing rings.
Keyclack sells unique silencing rings. These silencing rings are intended to be installed by placing them directly into the case and then inserting the sliders (other silencing rings are usually installed onto the slider first before inserting the slider into the case). Whether or not this design difference is noticeable is probably negligible.
KBDFans produces their own 0.3mm silencing rings.
Counteracting Travel Loss With Silencing Rings
When using silencing rings on stock Topre/HHKB (non-Type-S) sliders, a slight loss of travel may occur as a result of the thickness of the silencing rings. There are various methods of counteracting the loss in travel.
These precut gaskets fit around rubber domes to make up for the loss of travel. Deskeys sells these gaskets in various thicknesses associated with their silencing rings.
The Old Days
Before the advent of mass-produced silencing rings, there were a handful of options that are no longer considered worthwhile by most modders.
The first aftermarket silencing method I'm aware of were dental bands (commonly used for orthodontic adjustments). Dental bands can be applied to sliders just like silencing rings. The downside to dental bands are that they reduce key travel significantly (even on Type-S sliders) and tend to dry out and crack in a fairly short amount of time.
Another option common until newer mass-produced rings were those produced by community member Hypersphere, hand-made using a punch. Some users would use an iron to flatten these out more to reduce overall key travel reduction.