Unfortunately, yEd's SVG export does not allow for customizing how URLs are exported.
However, the links work for me even if the SVG document is not embedded in <object> tags. My test file was
<html>
<head>
<title>Test</title>
</head>
<body>
<p>Foo bar baz</p>
<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" fill-opacity="1" color-rendering="auto" color-interpolation="auto" text-rendering="auto" stroke="black" stroke-linecap="square" width="34" stroke-miterlimit="10" shape-rendering="auto" stroke-opacity="1" fill="black" stroke-dasharray="none" font-weight="normal" stroke-width="1" height="34" font-family="'Dialog'" font-style="normal" stroke-linejoin="miter" font-size="12px" stroke-dashoffset="0" image-rendering="auto">
<!--Generated by ySVG 2.5-->
<defs id="genericDefs"/>
<g>
<defs id="defs1">
<clipPath clipPathUnits="userSpaceOnUse" id="clipPath1">
<path d="M0 0 L34 0 L34 34 L0 34 L0 0 Z"/>
</clipPath>
<clipPath clipPathUnits="userSpaceOnUse" id="clipPath2">
<path d="M422 149 L456 149 L456 183 L422 183 L422 149 Z"/>
</clipPath>
</defs>
<g id="y.node.0">
<a target="_blank" xlink:type="simple" xlink:href="https://www.yworks.com/" xlink:show="new">
<g fill="rgb(255,204,0)" text-rendering="geometricPrecision" shape-rendering="geometricPrecision" transform="matrix(1,0,0,1,-422,-149)" stroke="rgb(255,204,0)">
<rect x="424" width="30" height="30" y="151" clip-path="url(#clipPath2)" stroke="none"/>
</g>
<g text-rendering="geometricPrecision" stroke-miterlimit="1.45" shape-rendering="geometricPrecision" transform="matrix(1,0,0,1,-422,-149)" stroke-linecap="butt">
<rect fill="none" x="424" width="30" height="30" y="151" clip-path="url(#clipPath2)"/>
</g>
<g>
<g text-rendering="geometricPrecision" stroke-miterlimit="1.45" shape-rendering="geometricPrecision" font-family="sans-serif" transform="matrix(1,0,0,1,-422,-149)" stroke-linecap="butt">
<text x="435.1826" xml:space="preserve" y="170.1543" clip-path="url(#clipPath2)" stroke="none">1</text>
</g>
</g>
</a>
</g>
</g>
</svg>
</body>
</html>
and I tested in Chrome 68.0.3440.84 and Firefox 61.0.1 on Ubuntu 16.04.