To be 100% sure, you can do online troubleshooting with a tool like DNSViz (or Zonemaster) both a standard test (using current nameservers) and an undelegated test (specifying the new nameserver and hence testing their configuration as if they were the authoritative one for the zone).
You can then assess if everything is in order, including DNSSEC aspect.
Had you specified directly the domain name you are considering, anyone could have tested things out for you...
You state "removing the DS record in the domain zone": the
DS record is at parent (the "registry") not in the zone itself. If, indeed, the parent has no
DS records for the specific name, then indeed
DNSSEC is disabled, and the presence of
RRSIG records in the zone is irrelevant, they will never be taken into account (do not that some security scanner may however report a problem here as considering their presence plus the absence of
DS at parent is a sign of a problem).
If everything is ok, you can indeed move the domain to new nameservers and there won't be any issues related to DNSSEC because DNSSEC is not there despite some records in the child zone.
You should however in the long run clean up things: either activate DNSSEC (do not just add a
DS record at registry, do check first with same check as above that everything matches) which should be the superior path, or decide once for all to skip DNSSEC and then remove any
NSEC3 records from your zone because they are useless.