Savlon antiseptic liquid was discontinued quite a few years ago by the manufacturer. Closer examination of the link provided will show that the product is no longer available and you'll not find it any shops in the UK. Nowadays, it's been replaced by products containing benzalkonium chloride and most of the marketed benzalkonium chloride containing antiseptics are either odourless or have a faint smell. That'll probably fit the bill. BC containing antiseptics are not quite as potent as the cetrimide/chlorhexidine combination that was in Savlon liquid but they do work reasonably well.
At uni, we make our own version of Savlon out of the raw ingredients but then again, I'm old enough to remember when we used to use Chloramine-T and Acriflavine in the labs as antiseptics. At one time, there was a first aid section at the back of a famous organic chemistry textbook that advised pouring Chloramine-T solution over every burn, abrasion and wound. Lovely stuff!