どうしようもない	1572389	97.2%
どうしようも無い	42341	2.6%
どう仕様もない	1348	0.1%
如何しようもない	957	0.1%
如何しようも無い	663	0.0%
どう仕様も無い	456	0.0%
如何仕様も無い	115	0.0%

1. Added a missing form(どうしようも無い), hid a bunch of rare forms, left どう仕様もない as [rK] so that kanji are visible for しよう and ない. 
2. Leading with my conclusion: I think 如何 for どう should be turned to [sK] for most entries that currently include it. (There seems to be an effort to include 如何, but its a bit haphazard and many どう　entries are currently missing it)

The rest is essentially a long-winded rational for 2.
===
Note: sankoku does not give kanji for どう anywhere. It does give 如何 for the いか... entries.

There may be a slightly bigger question about the inclusion of 如何 as an explicit surface form for どう across so many entries (other than どう itself, where it should obviously appear)。 Some of our entries do it(如何しても, 如何した, 如何した訳か, 如何してもと言うのなら), some don't (どうしたの, どうしたものか, どうしたら, どうしたもの, どうした風の吹き回しか). ngrams will return any of the latter group with 如何, though the percentages will of course be low.
どうしたの	923650	18.7%
如何したの	3532	0.1%

どうしたものか	303691	6.1%
如何したものか	1345	0.0%

どうしたら	3350666	67.7%
如何したら	6814	0.1%

どうしたもの	356667	7.2%
如何したもの	1780	0.0%

どうした風の吹き回しか	406	0.0%
如何した風の吹き回しか	0	0.0% <- not this one, I guess

This isn't an exhaustive list, and I don't see any rhyme or reason to it. 如何 is [rK] on the どう entry itself, it's always seemed like a bit of clutter to sprinkle 如何 all over the search results.

Most entries (including the advanced search in jmdictdb here, and jisho.org) will prominently display the kanji form even for [uk] entries.  I think this is as it should be, in general. But this seems a bit silly for どう:
https://jisho.org/search/如何　どう

And, if we coincidentally list one form without 如何, but with some other kanji (such as どう仕様もない), then that lucky entry will have 如何 suppressed, with the 'kanji' entry beginning with kana どう。

I've made a shorter [sK] suggestion on the どういう 如何言う entry as well, just to isolate the issue without all of my rambling:
どういう	9246980	98.2%
どう言う	160947	1.7%
如何いう	3333	0.0%. <-- can we [sK] this?
如何言う	1687	0.0%  <-- and this? 

Following this thought, I've left どうしようも無い at 2.6% as an ordinary kanji form, even though it's trivial and I wouldn't care at all about not displaying it(I think I've mentioned before that ない　and 無い should both be searchable, but I think it rarely matters to display the kanji...).  どう仕様もない as [rK] gives the kanji for 仕様.  I've [sK]'d everything else, which will hide 如何 as a surface form on this entry entirely. That's what I *think* should happen.  

Amusingly, the only kanji form daijs gives is 如何しようも無い, leaving 仕様 off entirely (which is the most-common-form (どう仕様もない) we previously fronted).  The daijs choice seems a bit arbitrary (not criticizing, these choices often are).

@@ -4,0 +5,3 @@
+<keb>どうしようも無い</keb>
+</k_ele>
+<k_ele>
@@ -5,0 +9 @@
+<ke_inf>&rK;</ke_inf>
@@ -8,0 +13 @@
+<ke_inf>&sK;</ke_inf>
@@ -11,0 +17 @@
+<ke_inf>&sK;</ke_inf>
@@ -14,0 +21 @@
+<ke_inf>&sK;</ke_inf>
@@ -17,0 +25 @@
+<ke_inf>&sK;</ke_inf>

G n-grams - see below

@@ -20,0 +21 @@
+<re_pri>spec1</re_pri>

OK

@@ -28 +28 @@
-<gloss>it's no use avoidng it</gloss>
+<gloss>it's no use fighting back</gloss>

I think "there is no other way" implies active effort but this phrase doesn't

@@ -28 +28 @@
-<gloss>there is no other way</gloss>
+<gloss>it's no use avoidng it</gloss>

GG5: There's nothing for it. | It's hopeless. | There is no help for it. | Nothing can be done about it. | There is no way out of it.
どう仕様も無い	456
どう仕様もない	1348
どうしようもない	1572389
如何しようも無い	663
如何仕様も無い	115
如何しようもない	957

GG5's "There is no way out of it" is much the same as "there is no other way".

@@ -3,0 +4,9 @@
+<k_ele>
+<keb>どう仕様もない</keb>
+</k_ele>
+<k_ele>
+<keb>如何しようもない</keb>
+</k_ele>
+<k_ele>
+<keb>如何しようも無い</keb>
+</k_ele>
@@ -8 +17 @@
-<keb>どう仕様もない</keb>
+<keb>如何仕様も無い</keb>
@@ -17,0 +27 @@
+<gloss>there's nothing for it</gloss>
@@ -18,0 +29,2 @@
+<gloss>it's hopeless</gloss>
+<gloss>there is no way out of it</gloss>

http://nihongo.monash.edu/cgi-bin/wwwjdic?1Q�ɤ����ͤ�̵��_0__

This is not quite 仕方ない
One of the meanings of どうしようもない is "impossible situation", "to have no chance at all", "to have no hope", "to be powerless"

助けてやりたいとは思うが、自分ではどうしようもなかった。
I wanted to help, but there was nothing I could do. 

どこに行ってもどうしようもないという感じになっていますね。
There is an air of resignation everywhere. 

万事休すだ。もうどうしようもない。
It is all over with me. It can't be helped. 

君って本当にどうしようもないね。
You really are hopeless. 

I'd even say "there is no other way" is wrong.

scriptscriptscript

@@ -15,0 +15,1 @@
+<pos>&adj-i;</pos>