Suppress Numbering of Subfigures

Because you don't need labels and numbers of subsubfigures, and I guess you don't need captions as well, you could simply use minipage environments or \parbox for those figures instead of nesting subfigures.

Further, if you use the subfigure package, which is outdated, you might consider to use the newer subfig or subcaption package instead.

A possible solution with the already mentioned »subcaption« package (shipped with caption).

\documentclass[11pt,a4paper,english]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{babel}
\usepackage[includeheadfoot,margin=3cm]{geometry}
\usepackage[font=small,labelfont=bf,tableposition=top]{caption}
\usepackage[font=footnotesize]{subcaption}
\usepackage{blindtext}

%\DeclareCaptionSubType*[arabic]{figure}
%\captionsetup[subfigure]{labelformat=simple,labelsep=colon}

\title{Two subfigures without a caption}
\author{Myx}

\begin{document}
  \maketitle

  \blindtext

  \begin{figure}[!ht]
    \centering
    \begin{subfigure}[b]{0.45\textwidth}
      \centering
      \rule{6.4cm}{3.6cm}
    \end{subfigure}
    \hfill
    \begin{subfigure}[b]{0.45\textwidth}
      \centering
      \rule{6.4cm}{3.6cm}
    \end{subfigure}
    \caption{Dummy figures}\label{fig:dummy}
  \end{figure}

  \blindtext
\end{document}