You can call the airlines and check if baggage connection option is available from the transfer counter located airside. In that case, after arriving at Singapore airside, you can visit transfer counter of onward airline and connect your bag and get boarding pass, airside.
UPDATE: As far as I'm aware there is no third-party baggage connection service in Singapore. Both GoAir and Scoot are low-cost carriers and do not interline.
The Visa Free Transit Facility (VFTF) is available for people with visa of specific countries.
From - https://www.ica.gov.sg/enteranddeparting/before/enteranddeparting_before_vftf
If you are in transit to or from any third country via Singapore, you
may be eligible for the 96-hour VFTF if you meet these requirements:
- You may enter Singapore by any mode of transport but depart only via air or sea.
- You must have a valid onward air/ferry/cruise ticket departing Singapore within 96 hours; and
- You must have a valid visa*/long-term pass (with a validity of at least 1 month from the date of entry into Singapore under the VFTF)
issued by any of the following countries:
- New Zealand
- United Kingdom
- United States of America
A visa is considered valid so long as it is good for entry into one of
the eight countries listed above. Travellers with Single Journey Visas
(SJV) may still be granted VFTF on the return leg of their journey
(i.e. after the SJV is used and no longer valid), but you must:
- Travel directly from the country that issued the SJV, en route through Singapore, back to your home country
- Not have returned to your home country since you last used the SJV.
^ Applies to visas issued by Germany or Switzerland, or Schengen visas
that are good for entry to Germany or Switzerland.