In the German Lilypond forum (now available in the archive) someone figured
out a solution, here a comparison of both solutions

\version "2.19.56"

soft =
-\tweak stencil
#(lambda (grob)
   (grob-interpret-markup grob
     (if (eq? UP (ly:grob-property grob 'direction))
         #{
           \markup
           \with-dimensions #'(-0.55 . 0.55) #'(-0.55 . 0)
           \postscript
           #"0.25 setlinewidth -0.55 0 moveto 0 0 0.55 180 0 arc stroke"
         #}
         #{
           \markup
           \with-dimensions #'(-0.55 . 0.55) #'(0 . 0.55)
           \postscript
           #"0.25 setlinewidth 0.55 0 moveto 0 0 0.55 0 180 arc stroke"
         #})))
-\accent

unaccent =
  -\tweak stencil #ly:text-interface::print
  -\tweak text \markup
  \translate #'(0.6 . 0)
  \stencil
    #(make-path-stencil
    '(M -0.435 0.435
      C -0.435 0.185 -0.250 0 0 0
      C  0.250 0 0.435 0.185 0.435 0.435)
    0.13 1 1 #f)
  -\accent

\relative c'' { c_\soft c^\soft c_\unaccent c^\unaccent }

2017-06-15 16:23 GMT+02:00 Pierre Perol-Schneider <
pierre.schneider.pa...@gmail.com>:

> Or - using Kieren's solution:
>
> \version "2.19"
>
> unaccent =
>   -\tweak stencil #ly:text-interface::print
>   -\tweak text \markup
>   \translate #'(0.6 . 0)
>   \stencil
>     #(make-path-stencil
>     '(M -0.435 0.435
>       C -0.435 0.185 -0.250 0 0 0
>       C  0.250 0 0.435 0.185 0.435 0.435)
>     0.13 1 1 #f)
>   -\accent
>
> {
>   f''\unaccent
> }
>
>
> 2017-06-15 16:07 GMT+02:00 Pierre Perol-Schneider <
> pierre.schneider.pa...@gmail.com>:
>
>> Hi caagr98,
>>
>> How about:
>>
>> \version "2.19"
>>
>> unaccent = -\markup
>>   \translate #'(0.6 . 0)
>>   \stencil
>>     #(make-path-stencil
>>     '(M -0.435 0.435
>>       C -0.435 0.185 -0.250 0 0 0
>>       C  0.250 0 0.435 0.185 0.435 0.435)
>>     0.13 1 1 #f)
>>
>> {
>>   f''^\unaccent
>> }
>>
>>
>> HTH, Cheers,
>> Pierre
>>
>> 2017-06-15 15:59 GMT+02:00 <caag...@gmail.com>:
>>
>>> On 06/15/2017 03:42 PM, Kieren MacMillan wrote:
>>>
>>>> Hi caagr98,
>>>>
>>>> I'd rather not have to install extra fonts for my scores to work...
>>>>>
>>>>
>>>> You don't have to install extra fonts — just find a font that's already
>>>> installed and has that glyph.
>>>>
>>>
>>> That's exactly what I mean - I don't want to depend on what fonts I have
>>> installed.
>>>
>>> Isn't there any way to do it with markup or stencils?
>>>>>
>>>>
>>>> Of course. Change
>>>>
>>>>      \markup \fontsize #1 \override #'(font-name . "Old Standard")
>>>> \char ##x23D1
>>>>
>>>> to whatever drawing routine you prefer.
>>>>
>>>
>>> Considering text-interface doesn't bother flipping the symbol
>>> upside-down, I think I'll have to replace the entire stencil. I'll make
>>> sure to report back when I've got it to work.
>>>
>>>
>>> Cheers,
>>>> Kieren.
>>>> ________________________________
>>>>
>>>> Kieren MacMillan, composer
>>>> ‣ website: www.kierenmacmillan.info
>>>> ‣ email: i...@kierenmacmillan.info
>>>>
>>>>
>>> _______________________________________________
>>> lilypond-user mailing list
>>> lilypond-user@gnu.org
>>> https://lists.gnu.org/mailman/listinfo/lilypond-user
>>>
>>
>>
>
> _______________________________________________
> lilypond-user mailing list
> lilypond-user@gnu.org
> https://lists.gnu.org/mailman/listinfo/lilypond-user
>
>
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