You can use SpriteBatch
to draw a single-pixel texture as you described--you could use a white texture and use the SpriteBatch tinting to make it Blue.
Here is some simple code for programmatically creating a 1x1 white texture in Direct3D 11:
Microsoft::WRL::ComPtr<ID3D11ShaderResourceView> pWhiteTexture;
static const uint32_t s_pixel = 0xffffffff;
D3D11_SUBRESOURCE_DATA initData = { &s_pixel, sizeof(uint32_t), 0 };
D3D11_TEXTURE2D_DESC desc;
memset( &desc, 0, sizeof(desc) );
desc.Width = desc.Height = desc.MipLevels = desc.ArraySize = 1;
desc.Format = DXGI_FORMAT_R8G8B8A8_UNORM;
desc.SampleDesc.Count = 1;
desc.Usage = D3D11_USAGE_IMMUTABLE;
desc.BindFlags = D3D11_BIND_SHADER_RESOURCE;
Microsoft::WRL::ComPtr<ID3D11Texture2D> tex;
HRESULT hr = mDevice->CreateTexture2D( &desc, &initData, &tex );
DX::ThrowIfFailed(hr);
D3D11_SHADER_RESOURCE_VIEW_DESC SRVDesc;
memset( &SRVDesc, 0, sizeof( SRVDesc ) );
SRVDesc.Format = DXGI_FORMAT_R8G8B8A8_UNORM;
SRVDesc.ViewDimension = D3D11_SRV_DIMENSION_TEXTURE2D;
SRVDesc.Texture2D.MipLevels = 1;
hr = mDevice->CreateShaderResourceView( tex.Get(), &SRVDesc, &pWhiteTexture );
DX::ThrowIfFailed(hr);
A more efficient solution would be to use PrimitiveBatch
to draw a blue quad where you want it located.
See the DirectX Tool Kit tutorial Simple rendering