Putting aside my personal feelings (on breeding and selling puppies), as well as the TOS for most payment gateways (including Shopify Payments) and focusing purely on the technical question at hand ...
I would recommend putting the product price as the 'reserve payment' price, and then making it VERY clear in the product description that the $199 is a reserve/deposit fee, and that the actual price is $XXX.XX.
Then once you get an order (from a customer who pays the reserve/deposit), you can send them a 'draft order' for the remaining amount.
If you wanted to get really fancy, you could get a Shopify Design Expert to add a bit of code to your product page template, so that it shows something like this:
"$199 DEPOSIT ($XXX.XX FULL PRICE)"
Where the '$XXX.XX' value is a multiplier of the main product price.
ex. $199 DEPOSIT ($995 FULL PRICE) -- where the '$995' is generated by multiplying the deposit price ($199) by 5. So then if you're selling different products with different prices, then it will always automatically show the full price as a multiplier of the actual price (ie. reserve price).
Hope this makes sense and helps!