Not quite. In this circumstance it's most likely that Dogs initiated the release (disclaimer - has any of this actually happened yet?) and Woods is within his right to say "you signed, you pay" so onus is on Dogs to appease Woods. Someone would put feelers out if any club is willing to take the contract of Woods, then the Dogs have to check with Woods if that club is agreeable with him. So Woods has 100% choice from those available clubs (or 0% if Dogs can't come to an adequate deal), and there could be a plethora of reasons of choosing Sharks over anyone else. Either way Woods is still getting paid what he signed for, so it's up to Dogs to negotiate with Sharks on how much each club pays to that amount. Now Ram may be correct because of course the Sharks would try to lowball the Dogs, but at what stage do Dogs back out because moving him on hurts them more than keeping him? Especially when they have other options that they could move on e.g. Klemmer, that could move it more from a buyers markets/firesale.
The only way I could see Sharks paying half, besides Dogs losing their minds, is if Dogs are paying fully this and next, effectively writing off both seasons. Not so much an issue this season but I'd have to look into when their board are up for reelection to see if they'd willingly play for $800/$900/$whatever under the cap and likely having another bad season